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Finding Side Lengths Using the Law of Sines

Total questions: 10

Worksheet time: 5mins

Name
Class
Date
1.

A triangle has angles A = 30° and B = 45°. If side a = 10 cm, find the length of side b using the law of sines.

a)

10√2 cm

b)

5 cm

c)

15 cm

d)

20 cm

2.

In triangle ABC, angle A = 50° and angle B = 60°. If side a = 12 m, calculate the length of side b.

a)

14.0 m

b)

10.5 m

c)

16.2 m

d)

12.5 m

3.

A boat sails from point A to point B, creating a triangle with angle A = 70° and angle B = 40°. If the distance from A to C (the point directly across from B) is 15 km, find the distance from A to B.

a)

25.30 km

b)

30.00 km

c)

18.50 km

d)

21.92 km

4.

In triangle XYZ, angle X = 35° and angle Y = 75°. If side x = 20 m, use the law of sines to find the length of side y.

a)

25.50 m

b)

40.20 m

c)

30.75 m

d)

34.64 m

5.

A surveyor measures angle A = 55° and angle B = 85° in triangle ABC. If side a = 25 ft, determine the length of side b.

a)

28 ft

b)

40 ft

c)

20 ft

d)

32.5 ft

6.

A triangular park has angles measuring 45°, 60°, and 75°. If the side opposite the 45° angle is 30 m, find the lengths of the other two sides.

a)

b ≈ 36.74 m, c ≈ 41.00 m

b)

b ≈ 40.00 m, c ≈ 50.00 m

c)

b ≈ 30.00 m, c ≈ 45.00 m

d)

b ≈ 25.00 m, c ≈ 35.00 m

7.

In triangle DEF, angle D = 40° and angle E = 70°. If side d = 18 cm, calculate the length of side e using the law of sines.

a)

18.75 cm

b)

26.28 cm

c)

22.15 cm

d)

30.50 cm

8.

A ladder leans against a wall forming a triangle with the ground. If the angle between the ladder and the ground is 60° and the distance from the wall to the base of the ladder is 5 m, find the length of the ladder.

a)

12 m

b)

10 m

c)

8 m

d)

15 m

9.

In triangle PQR, angle P = 30° and angle Q = 50°. If side p = 10 m, find the length of side q using the law of sines.

a)

12.50 m

b)

18.75 m

c)

15.32 m

d)

20.00 m

10.

A triangle has angles measuring 30°, 60°, and 90°. If the side opposite the 30° angle is 5 m, find the lengths of the other two sides.

a)

5 m and 15 m

b)

The lengths of the other two sides are 5√3 m and 10 m.

c)

10√2 m and 5 m

d)

7 m and 12 m