Mastering Angles & Sides: The Law of Sines Challenge

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

• 60 degrees

• 30 degrees

• 90 degrees

• 48.59 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.

• 50 degrees

• 15 degrees

• 22.6 degrees

• 30 degrees

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

• 12.50 km

• 10.39 km

• 15.75 km

• 8.25 km

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

• 53.13 degrees

• 75 degrees

• 60 degrees

• 45 degrees

In triangle XYZ, angle X is 40 degrees, side x is 20 m, and side y is 25 m. Find the measure of angle Y.

• 90 degrees

• 30 degrees

• 50 degrees

• 70 degrees

A triangle has sides measuring 7 m, 10 m, and 12 m. Determine the angles of the triangle using the law of sines.

• Angles are approximately 45°, 60°, and 75°.

• Angles are approximately 20°, 70°, and 90°.

• Angles are approximately 50°, 80°, and 50°.

• Angles are approximately 30.5°, 47.5°, and 101.9°.

A lighthouse is located at point A, and a ship is at point B. The angle at the lighthouse (angle A) is 75 degrees, and the distance from the lighthouse to the ship (side a) is 100 m. If the distance from the ship to point C (side b) is 80 m, find angle B.

• 65 degrees

• 30 degrees

• 90 degrees

• 50.5 degrees

In triangle DEF, angle D is 30 degrees, side d is 15 m, and side e is 20 m. Calculate the measure of angle E using the law of sines.

• 41.81 degrees

• 50 degrees

• 60 degrees

• 25 degrees

A triangle has angles measuring 35 degrees and 65 degrees. If the side opposite the 35-degree angle is 9 m, find the length of the side opposite the 65-degree angle.

• 8.75 m

• 12.24 m

• 10.50 m

• 15.00 m

A construction worker needs to find the height of a building. He measures a distance of 50 m from the base of the building to a point where he sees the top at an angle of elevation of 60 degrees. Using the law of sines, calculate the height of the building.

• 100.0 m

• 75.0 m

• 86.6 m

• 60.0 m