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Mastering Sines and Cosines: Triangles in Action

Total questions: 10

Worksheet time: 5mins

Name
Class
Date
1.

A triangle has two sides measuring 8 cm and 10 cm, with an included angle of 45 degrees. What is the length of the third side?

a)

c = 15 cm

b)

c = √(164 - 80√2) cm

c)

c = 6 cm

d)

c = 12 cm

2.

In triangle ABC, angle A measures 30 degrees, side a is 12 cm, and side b is 15 cm. Calculate the measure of angle B using the law of sines.

a)

25 degrees

b)

38.68 degrees

c)

60 degrees

d)

45 degrees

3.

A ship sails from point A to point B, which is 50 km away. It then sails to point C, which is at an angle of 60 degrees from point B. If the distance from B to C is 40 km, how far is point A from point C?

a)

45.83 km

b)

60 km

c)

30 km

d)

70 km

4.

In triangle XYZ, angle X is 40 degrees, angle Y is 70 degrees, and side x is 15 m. Find the length of side y using the law of sines.

a)

22.1 m

b)

18.5 m

c)

20.0 m

d)

25.3 m

5.

A ladder leans against a wall, forming a 75-degree angle with the ground. If the foot of the ladder is 4 m from the wall, how long is the ladder?

a)

15.5 m

b)

12 m

c)

18 m

d)

10 m

6.

A triangle has sides of lengths 7 m and 9 m, with an angle of 50 degrees between them. Use the law of cosines to find the length of the third side.

a)

8.3 m

b)

9.5 m

c)

7.1 m

d)

6.5 m

7.

In a triangle, angle A is 50 degrees, side a is 10 m, and side b is 15 m. Find angle B using the law of sines.

a)

40 degrees

b)

30 degrees

c)

60 degrees

d)

20 degrees

8.

A surveyor measures a triangular plot of land. One side is 100 m, and the angles opposite to this side are 30 degrees and 60 degrees. Calculate the length of the other two sides.

a)

b = 150 m, c = 180 m

b)

b = 120 m, c = 160 m

c)

b = 173.21 m, c = 200 m

d)

b = 200 m, c = 250 m

9.

A kite is flying at an angle of elevation of 30 degrees from a point on the ground. If the string of the kite is 50 m long, how high is the kite above the ground?

a)

40 m

b)

35 m

c)

15 m

d)

25 m

10.

In triangle DEF, angle D is 45 degrees, side d is 10 cm, and side e is 12 cm. Calculate the measure of angle E using the law of sines.

a)

36.87 degrees

b)

30 degrees

c)

50 degrees

d)

60 degrees