Mastering Sines and Cosines: Triangles in Action

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?

• c = 15 cm

• c = √(164 - 80√2) cm

• c = 6 cm

• c = 12 cm

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.

• 25 degrees

• 38.68 degrees

• 60 degrees

• 45 degrees

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?

• 45.83 km

• 60 km

• 30 km

• 70 km

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.

• 22.1 m

• 18.5 m

• 20.0 m

• 25.3 m

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?

• 15.5 m

• 12 m

• 18 m

• 10 m

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.

• 8.3 m

• 9.5 m

• 7.1 m

• 6.5 m

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.

• 40 degrees

• 30 degrees

• 60 degrees

• 20 degrees

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.

• b = 150 m, c = 180 m

• b = 120 m, c = 160 m

• b = 173.21 m, c = 200 m

• b = 200 m, c = 250 m

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?

• 40 m

• 35 m

• 15 m

• 25 m

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.

• 36.87 degrees

• 30 degrees

• 50 degrees

• 60 degrees