SINE AND COSINE RULES – PRACTICE QUESTIONS
1.
Use sine rule to find x to 1 decimal place.
x
13.9 cm
49°
62°
2.
Use sine rule to find y to 1 decimal place.
58°
y
51°
7.2 m
3.
Use sine rule to find z to 2 significant figures.
z
11 cm
31°
65°
4.
Use cosine rule to find a to the nearest centimetre.
21°
12.3 cm
16.1 cm
a
5.
Use cosine rule to find b to 3 significant figures.
b
9.9 m
48°
17.1 m
6.
Use cosine rule to find c to 2 decimal places.
16.6 m
c
63°
25.5 m
7.
Use sine rule to find d to 2 significant figures.
d
16.1 cm
41°
24.5 cm
8.
Use sine rule to find e to the nearest degree.
8.4 cm
7 cm
e
57°
9.
Use sine rule to find f to 2 significant figures.
64°
8.1 cm
f
14.5 cm
10.
Use cosine rule to find g to 2 significant figures.
56 cm
70 cm
g
91 cm
11.
Use cosine rule to find h to 2 significant figures.
11.1 m
18.9 m
h
10.8 m
12.
Find x to 3 significant figures.
9.8 m
x
70°
43°
13.
Find y to 1 decimal place.
65°
8.2 cm
7.6 cm
y
14.
Find z to 1 decimal place.
z
16 cm
46°
17 cm
15.
Find x to 3 significant figures.
13.8 cm
15.4 cm
x
40°
16.
Find y to 1 decimal place.
8.1 m
14.7 m
y
15.3 m
17.
Find z to 2 significant figures.
41°
560 m
470 m
z
18.
Find x to 3 significant figures.
36 cm
x
44°
51°
19.
Find y to 3 significant figures.
y
98 cm
209 cm
247 cm
20.
Find z to 2 significant figures.
75 cm
47°
68 cm
z
21.
Find the area of the triangle. Give your answer to 3 significant figures.
61°
15 cm
12 cm
22.
Find the area of the triangle. Give your answer to the nearest square centimetre.
16.6 cm
50°
19.7 cm
23.
ABC is a triangle.
The area of ABC is 96 cm2.
Find the size of angle BAC to the nearest unit.
A
17.8 cm
B
19.3 cm
C
24.
DEF is a triangle, with an area of 225 cm2.
Find the size of angle DFE. Give your answer to 2 significant figures.
D
26.2 cm
F
38.5 cm
E
25.
Find the area of triangle GHI.
Give your answer to the nearest square centimetre.
G
4.5 cm
33°
3.2 cm
76°
I
H
I
26.
JKL and KML are triangles.
Find the size of the angle KML. Give your answer to 2 significant figures.
M
K
50°
32.1 m
10.7 m
69°
J
19°
L
27.
NOP and OQP are triangles.
Find the size of QP, to 3 significant figures.
Q
O
58°
61°
21.8 cm
38°
N
P
29.7 cm
28.
Find the area of the triangle. Give your answer to the nearest square centimetre.
9.0 cm
13.5 cm
14.4 cm