Mastering Missing Angles with the Law of Sines

A triangle has one angle measuring 30 degrees and the side opposite this angle is 10 meters long. If the side opposite the unknown angle is 15 meters, what is the measure of the unknown angle?

• 48.59 degrees

• 90 degrees

• 60 degrees

• 30 degrees

In a triangle, angle A measures 45 degrees, side a is 8 cm, and side b is 10 cm. Use the law of sines to find the measure of angle B.

• 22.6 degrees

• 30 degrees

• 50 degrees

• 15 degrees

A boat is sailing from point A to point B, creating a triangle with point C. If angle A is 60 degrees, angle C is 50 degrees, and side a (opposite angle A) is 12 km, how long is side c (opposite angle C)?

• 10.39 km

• 15.75 km

• 12.50 km

• 8.25 km

A surveyor measures a triangle where angle A is 70 degrees, side a is 25 meters, and side b is 30 meters. Calculate the measure of angle B using the law of sines.

• 60 degrees

• 45 degrees

• 75 degrees

• 53.13 degrees

In triangle XYZ, angle X is 40 degrees, side x is 5 m, and side y is 7 m. What is the measure of angle Y?

• 57.8 degrees

• 75 degrees

• 90 degrees

• 30 degrees

A ladder leans against a wall, forming a triangle with the ground. If the angle between the ladder and the ground is 75 degrees and the ladder is 10 feet long, how high up the wall does the ladder reach?

• 9.66 feet

• 7.2 feet

• 10.5 feet

• 8.5 feet

A triangular park has one angle measuring 50 degrees and the side opposite this angle is 20 meters. If another side is 25 meters long, find the measure of the angle opposite the 25-meter side.

• 90 degrees

• 61.5 degrees

• 75 degrees

• 45 degrees

In triangle ABC, angle A is 30 degrees, side a is 10 m, and side b is 15 m. Use the law of sines to find angle B.

• 48.59 degrees

• 75 degrees

• 30 degrees

• 60 degrees

A kite is flying at an angle of elevation of 45 degrees from a point on the ground. If the string of the kite is 50 meters long, how high is the kite above the ground?

• 45 meters

• 35.36 meters

• 60 meters

• 25 meters

A triangle has sides measuring 12 m, 16 m, and an unknown angle opposite the 12 m side. If the angle opposite the 16 m side is 70 degrees, find the unknown angle using the law of sines.

• 30 degrees

• 60 degrees

• 44.4 degrees

• 90 degrees