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The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence Name: HW1 – Grade B Homework on Trigonometry - higher 1. (a) Teacher Assessment The diagram shows a right-angled triangle ABC. AB = 10 cm and AC = 15 cm C 15 cm Not drawn accurately B A 10 cm Calculate the length of BC. Leave your answer as a square root. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer .................................................................. cm (3) (b) The diagram shows a right-angled triangle DEF. EF = 10 cm Angle F = 50° D Not drawn accurately E 50° 10 cm Angle Sine Cosine Tangent 40° 0.643 0.766 0.839 50° 0.766 0.643 1.192 F Use the table of data to work out the length of DE. ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... ...................................................................................................................................... Answer .................................................................. cm (3) (Total 6 marks) The Robert Smyth School 1 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 2. Use the information in the table to calculate the value of x. Not drawn accurately sin 60° = 0.866 60° 5 cm x cos 60° = 0.5 tan 60° = 1.732 ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ................................................................ cm (3) (Total 3 marks) 3. The diagram shows a triangle ABC. Angle A = 20° and angle C = 90° AB = 32 m B 32 m 20º A C Not drawn accurately Calculate the height BC. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ....................................................................m (Total 3 marks) The Robert Smyth School 2 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 4. ABC is a right-angled triangle. AB = 51 cm Angle CAB = 48° B 51 cm A Not to scale 48° C Find the length of BC. Give your answer to a suitable degree of accuracy. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ................................................................ cm (Total 4 marks) 5. ABC is a right-angled triangle. AB = 60 m Angle BAC = 32° B C 60 m Not drawn accurately 32° A Find the length of BC. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer .................................................... m (Total 3 marks) The Robert Smyth School 3 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 6. ABC is a right-angled triangle. BC = 125 m. Angle CAB = 33°. C Not drawn accurately x A 125 m 33º B Find the length of AC (marked x in the diagram). Give your answer to an appropriate degree of accuracy. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. Answer ............................................................ m (Total 4 marks) 7. (a) In triangle PQR, angle Q is a right angle. Angle R = 22° and PR = 18.3 cm P Not drawn accurately 18.3 cm 22° Q R Calculate the length of QR. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer …………………………..................... cm (3) The Robert Smyth School 4 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence (b) In triangle XYZ, angle Y = 90° XY = 10 cm and YZ = 3 cm X 10 cm Y Not drawn accurately 3 cm Z Work out the size of angle Z. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer …………………………………… degrees (3) (Total 6 marks) 8. PQ is the surface of a ramp laid on level ground. The ramp is 230 cm long and 20 cm high, as shown in the diagram. Q 230 cm x P Work out the size of angle x. Not to scale 20 cm R ......……….............................................................................................................................. ......……….............................................................................................................................. ......……….............................................................................................................................. ......……….............................................................................................................................. ......……….............................................................................................................................. Answer ................................................... degrees (Total 3 marks) The Robert Smyth School 5 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 9. In the diagram, PQ = 14 cm and QR = 8.6 cm. Angle PSQ = angle SQR = 90° Angle PQS = 25° P Not drawn accurately 14 cm S 25° Q 8.6 cm R Calculate angle R. ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer ................................................... degrees (Total 5 marks) Success: The Robert Smyth School Target: 6 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence HW2 – Grade B Homework on Trigonometry in context - higher 1. Teacher Assessment For a ladder to be safe it must be inclined at between 70° and 80° to the ground. (a) The diagram shows a ladder resting against a wall. 5.59 m 1.5 m Not to scale Is it safe? You must show your working. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (b) Another ladder rests against a wall. Work out the closest distance that the bottom of the ladder can be from the wall so that it is safe. ........................................................................................................................... ........................................................................................................................... 4m ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Answer ..................................................................... m (3) (Total 6 marks) The Robert Smyth School 7 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 2. (a) Sadhia stands 25 in from the base of a tree. The angle of elevation of the top of the tree is 17’. T not drawn accurately S 17° G 25 m Calculate the height of the tree, TG. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer......................................................................................................................m (3) (b) Max is holding the string of a kite which is flying 3O metres above the ground. His height is 1.5 metres. The string is straight and its length is 35 metres. K not drawn accurately 35 m 30 m x 1.5 m M L Calculate the angle x between the string and the ground. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer x = degrees (3) (Total 6 marks) The Robert Smyth School 8 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 3. (a) ABC is a right-angled triangle. AB = 5.1 cm CAB = 48° B 5.1 cm x Not drawn accurately 48° A C Find the length of BC (marked x in the diagram). Give your answer to a suitable degree of accuracy. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer ..................................... cm (4) (b) PQRS is a parallelogram. PQ = 5.1 cm PS = 6.8 cm QPS = 48° Q R 5.1 cm Not drawn accurately 48° P 6.8 cm S Calculate the area of PQRS. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer .................................... cm2 (2) (Total 6 marks) The Robert Smyth School 9 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 4. (a) A ramp is 4 metres long and 29 centimetres high. If the ramp is safe for wheelchair users the angle marked x must be 4 or less. not drawn accurately 4m 29 cm x Is this ramp safe for wheelchair users? You must show your working ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... Answer .................................................... (4) (b) The point A is 50 metres from the base of a tower. The angle of elevation of the top of the tower from A is 74. Tower not drawn accurately A 74° 50 m (i) Calculate the height of the tower. Give your answer to a suitable degree of accuracy. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... Answer .................................................... m (4) (ii) What is the angle of depression of the point A from the top of the tower? ........................................................................................................................... ........................................................................................................................... Answer .................................................... degrees (1) (Total 9 marks) The Robert Smyth School 10 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 5. The diagram shows two right-angled triangles. AD = 15 cm and CD = 6cm. A Not to scale 15 cm x° B y° D 6 cm C (a) Given that cos x° = 2 , calculate the length BD. 3 ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer BD = ............................................ (2) (b) Find the value of sin y°. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. ...............…………………………………………………………………………….. Answer sin y° = ............................................ Success: The Robert Smyth School Target: (3) (Total 5 marks) 11 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence HW3 – Grade A Homework on Trigonometry in 3D - Higher 1. Teacher Assessment The diagram shows a door-wedge with a rectangular horizontal base PQRS. The sloping face PQTU is also rectangular. PQ = 3.8 cm and angle TQR = 6° The height TR is 2.5 cm. U T 2.5 cm S Not drawn accurately R 6° P 3.8 cm Q Calculate the length of the diagonal PT. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ................................................................. cm (Total 5 marks) Use the space below to draw any extra triangles that will help in solving this question: The Robert Smyth School 12 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 2. VABCD is a right pyramid on a rectangular base. VA = VB = VC = VD = 16 cm. AB = 20 cm and BC = 14 cm. V Not drawn accurately 16 cm D C 14 cm A B 20 cm Calculate the angle between the edge VC and the base ABCD. ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer ........................................................... degrees (Total 5 marks) Use the space below to draw any extra triangles that will help in solving this question: The Robert Smyth School 13 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 3. VABCD is a right pyramid on a rectangular base. VA = VB = VC = VD = 11 cm. 0AB= 12 cm and BC = 7 cm. VO is the perpendicular height. V not drawn accurately 11 cm D C 7 cm O A 12 cm B Calculate the angle between the edge VB and the base ABCD. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer......................................................................................................................degrees (Total 5 marks) Use the space below to draw any extra triangles that will help in solving this question: The Robert Smyth School 14 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 4. VABCD is a right pyramid on a square base. V is vertically above the centre of the square. VA = VB = VC = VD = 20 cm AB = 15 cm V Not drawn accurately 20 cm D A 15 cm C B Calculate the angle between the edge VA and the base ABCD. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... Answer ......................................................... degrees (Total 5 marks) Use the space below to draw any extra triangles that will help in solving this question: The Robert Smyth School 15 The Robert Smyth School Mathematics Faculty Topic 4 Trigonometry Innovation & excellence 5. ABCDEFGH is a cuboid with sides of 5 cm, 5 cm and l2 cm as shown. A 5 cm B D C E Not to scale 5 cm F H 12 cm G Calculate angle DFH. ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer ............................................... degrees (Total 5 marks) Use the space below to draw any extra triangles that will help in solving this question: Success: The Robert Smyth School Target: 16
