Download Math 2201 Unit 3: Acute Triangle Trigonometry review sheet Sept 30

Math 2201 Unit 3: Acute Triangle Trigonometry review sheet
Sept 30-13
1.
Sketch a triangle that corresponds to the equation. Then, determine the third angle measure and the third side
length.
2.
Determine the length of d to the nearest tenth of a centimetre.
3. Determine the measure of  to the nearest degree.
4.
In QRS, r = 4.1 cm, s = 2.7 cm, and R = 88°. Determine the measure of Q to the nearest degree.
5.
In WXY, the values of w, x, and y are known. Write the form of the cosine law you could use to solve for the
angle opposite w.
6.
Determine the measure of  to the nearest degree.
7.
In DEF, d = 12.0 cm, e = 10.8 cm, and f = 12.4 cm. Determine the measure of D to the nearest degree.
8.
Solve for the unknown angle measure. Round your answer to the nearest degree.
9.
In a parallelogram, two adjacent sides measure 20 cm and 27 cm. The shorter diagonal is 23 cm. Determine, to
the nearest degree, the measures of the larger angles in the parallelogram.
10.
In TUV, U = 60°, u = 8.7 m, and v = 7.6 cm. Solve the triangle. Round angles to the nearest degree and sides
to the nearest tenth of a metre. Show your work.
11.
The pendulum of a grandfather clock is 90.0 cm long. When the pendulum swings from one side to the other side,
it travels a horizontal distance of 9.2 cm. Determine the angle through which the pendulum swings. Round your
answer to the nearest tenth of a degree.
12.
A parallelogram has sides that are 10 cm and 12 cm long. One of the angles in the parallelogram
measures 55°. Determine the length of the shorter diagonal to the nearest tenth of a centimetre.
13.
Determine the perimeter of the triangle to the nearest tenth of a centimetre.
14.
A radio tower is supported by two wires on opposite sides. On the ground, the ends of the wire are 46.5 m apart.
One wire makes a 62° angle with the ground. The other makes a 68° angle with the ground.
Draw a diagram of the situation. Then, determine the height of the tower to the nearest tenth of a metre.
15. Determine the perimeter of this quadrilateral to the nearest tenth of a centimetre.
2201 review sheet
Answer Section
SHORT ANSWER
1. ANS:
70°, 33.2
PTS: 1
DIF: Grade 11
REF: Lesson 3.1
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.3 Solve a
contextual problem that requires the use of the sine law or cosine law, and explain the reasoning.
TOP: Side-angle relationships in acute triangles
KEY: primary trigonometric ratios
2. ANS:
d = 6.2 cm
PTS: 1
DIF: Grade 11
REF: Lesson 3.2
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the sine law KEY: sine law
3. ANS:
 = 69°
PTS: 1
DIF: Grade 11
REF: Lesson 3.2
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the sine law KEY: sine law
4. ANS:
Q = 51°
PTS: 1
DIF: Grade 11
REF: Lesson 3.2
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the sine law KEY: sine law
5. ANS:
cos W =
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.2 Explain the
steps in a given proof of the sine law or cosine law.
TOP: Proving and applying the cosine law
KEY: cosine law
6. ANS:
 = 57°
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the cosine law
KEY: cosine law
7. ANS:
D = 62°
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the cosine law
KEY: cosine law
8. ANS:
76o
PTS: 1
9. ANS:
124o
PTS: 1
PROBLEM
10. ANS:
The measure of V is 49°.
T + U + V = 180°
T + 60° + 49° = 180°
T = 71°
The length of t is 9.5 m.
PTS: 1
DIF: Grade 11
REF: Lesson 3.2
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.3 Solve a
contextual problem that requires the use of the sine law or cosine law, and explain the reasoning.
TOP: Proving and applying the sine law KEY: sine law
11. ANS:
a2
9.22
84.64
–16 115.36
= b2 + c2 – 2bc cos A
= 90.02 + 90.02 – 2(90.0)(90.0) cos A
= 8100.00 + 8100.00 – 16 200.00 cos A
= –16 200.00 cos A
= cos A
A = cos–1(0.9947...)
A = 5.859...°
The pendulum swings through an angle of 5.9°.
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.3 Solve a
contextual problem that requires the use of the sine law or cosine law, and explain the reasoning.
TOP: Proving and applying the cosine law
KEY: cosine law
12. ANS:
The shorter diagonal, x, is opposite the smaller angle in a parallelogram. Use the cosine law to determine the
length of the diagonal.
x2 = 102 + 122 – 2(10)(12) cos 55°
x2 = 100 + 144 – 240(0.5735...)
x2 = 106.341...
x = 10.312...
The length of the shorter diagonal is 10.3 cm.
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.3 Solve a
contextual problem that requires the use of the sine law or cosine law, and explain the reasoning.
TOP: Proving and applying the cosine law
KEY: cosine law
13. ANS:
e2 = d2 + f2 – 2df cos E
e2 = 4.52 + 5.52 – 2(4.5)(5.5) cos 73°
e2 = 20.25 + 30.25 – 49.50(0.2923...)
e2 = 36.027...
e = 6.002...
Perimeter = d + e + f
Perimeter = 4.5 + 6.002... + 5.5
Perimeter = 16.002...
The perimeter of the triangle is 16.0 cm.
PTS: 1
DIF: Grade 11
REF: Lesson 3.3
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning.
TOP: Proving and applying the cosine law
KEY: cosine law
14. ANS:
Let the x and y be the lengths of the wires and h be the height of the tower.
The third angle is 180° – 62° – 68° = 50°.

Use the sine law to determine the length of one of the wires:
Use the sine ratio to determine the height of the tower:
The tower is 49.7 m tall.
PTS: 1
DIF: Grade 11
REF: Lesson 3.4
OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. | 3.3 Solve a
contextual problem that requires the use of the sine law or cosine law, and explain the reasoning. | 3.4 Solve a
contextual problem that involves more than one triangle.
TOP: Solving problems using acute
triangles
KEY: sine law| primary trigonometric ratios
15. ANS:
EF2 = EH2 + FH2 – 2EH·FH cos EHF
EF2 = 71.62 + 54.02 – 2(71.6)(54.0) cos 50°
EF2 = 5126.56 + 2916.00 – 7732.80(0.6427…)
EF2 = 3072.011…
EF = 55.425…

Perimeter = EF + FG + GH + HE
Perimeter = 55.425… + 70.451… + 73.5 + 71.6
Perimeter = 270.977…
The perimeter of EFGH is 271.0 cm.
PTS: 1
DIF: Grade 11
REF: Lesson 3.4
OBJ: 3.3 Solve a contextual problem that requires the use of the sine law or cosine law, and explain the
reasoning. | 3.4 Solve a contextual problem that involves more than one triangle.
TOP: Solving problems using acute triangles
KEY: sine law| cosine law