Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Maths Quest A Year 11 for Queensland WorkSHEET 5.2 Chapter 5 Right-angled triangles and trigonometry WorkSHEET 5.2 1 Right-angled triangles and trigonometry Name: ___________________________ 1 With respect to the labelled angle, state: (a) hypotenuse (b) adjacent side (c) opposite side 2 Express the following angles in degrees, minutes and seconds. (a) 15.2 (b) 15 12 (c) (d) tan 1 6.25 sin 1 54 (a) hypotenuse = SP (b) adjacent side = ST (c) opposite side = PT Use (DMS) or (o ’ ”) button on calculator. (a) 15.2 15 12 (b) 15 12 15.5 15 30 tan 1 6.25 (c) 80.9097 80 5435 sin 1 54 (d) sin 1 0.8 53.13 53 7 48 3 Calculate the following correct to two decimal places. 1 (a) tan 30 (b) (c) (d) 23 cos 4 5 (a) (b) (c) 75 sin 45 35 (d) 1 sin 67 5437 1 tan 30 1.73 23 cos 4 5 22.94 75 sin 45 35 106.07 1 sin 67 5437 37.77 Maths Quest A Year 11 for Queensland Chapter 5 Right-angled triangles and trigonometry WorkSHEET 5.2 2 (a) Using Pythagoras’ Theorem: 4 hypot. 2 base 2 ht 2 x 2 52 52 25 25 50 Determine the length of the unknown side in the triangle above using: (a) Pythagoras’ Theorem (b) trigonometry x 50 7.07 cm (b) opp. hypot. 5 x x sin 45 5 5 x sin 45 7.07 cm sin 45 5 Find the values of unknown marked sides correct to two decimal places. 6 2 Find the value of angle correct to one decimal cos = place. 5 cos = 0.4 = 66.4° x 8 x = 8 cos 27° x = 7.13 y sin 27° = 8 y = 8 sin 27° y = 3.63 cos 27° = 4 2 Maths Quest A Year 11 for Queensland 7 Chapter 5 Right-angled triangles and trigonometry WorkSHEET 5.2 A 6 m-long ladder rests against a vertical wall and forms an angle of 40° to the horizontal ground. How high up the wall does the ladder reach, correct to two decimal places? 3 2 h 6 h = 6 sin 40° h = 3.86 m (correct to two decimal places) sin 40° = 8 A large heavy drum is pushed 3.5 m up an inclined plane. If the inclined plane rises 2 m vertically, find the angle the inclined plane makes with the horizontal. 2 2 3 .5 sin = 0.5714 = 34.8° sin = 9 A 1.08 m-tall child flies a kite with 100 m of released string which makes an angle of 70° with the horizontal. How high is the kite flying? 3 h 100 h = 100 sin 70° h = 9397 m So, height of kite = 9397 1.08 m = 95.05 m sin 70° = Maths Quest A Year 11 for Queensland 10 Chapter 5 Right-angled triangles and trigonometry WorkSHEET 5.2 The angle of depression of a boat from a cliff 60 m high is 10°. How far is the boat from the base of the cliff? 4 2 60 d 60 d= tan 10 d = 340 m tan 10° =