Mastering Triangle Properties: Law of Sines Quiz

A triangle has angles A, B, and C. If angle A is 30 degrees and angle B is 70 degrees, what is the measure of angle C?

• 60 degrees

• 100 degrees

• 90 degrees

• 80 degrees

In triangle ABC, side a is 10 cm, angle A is 45 degrees, and angle B is 60 degrees. Calculate the length of side b using the law of sines.

• 8.500 cm

• 15.000 cm

• 10.500 cm

• 12.247 cm

A boat sails from point A to point B, creating a triangle with point C on the shore. If angle A is 50 degrees, angle B is 70 degrees, and side a (the distance from A to C) is 200 meters, how far is the boat from point B?

• 232.4 meters

• 300 meters

• 180 meters

• 150 meters

In a triangle, angle A measures 40 degrees, side a is 15 m, and side b is 20 m. Use the law of sines to find angle B.

• 90 degrees

• 45 degrees

• 30 degrees

• 60 degrees

A surveyor measures a triangle formed by three points. If angle A is 35 degrees, side a is 50 m, and side b is 70 m, what is angle B?

• 90 degrees

• 70 degrees

• 45 degrees

• 57.8 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 m long, how high does the ladder reach on the wall?

• 9.659 m

• 7.200 m

• 10.000 m

• 8.500 m

In triangle XYZ, angle X is 60 degrees, angle Y is 50 degrees, and side x is 12 m. Find the length of side y using the law of sines.

• 12.50 m

• 8.25 m

• 10.39 m

• 9.75 m

A triangular park has one angle measuring 80 degrees and two sides measuring 30 m and 45 m. Calculate the measure of the third angle and the length of the remaining side.

• Third angle: 100 degrees, Remaining side: 25.5 m

• Third angle: 90 degrees, Remaining side: 35 m

• Third angle: 120 degrees, Remaining side: 40 m

• Third angle: 80 degrees, Remaining side: 30 m

A triangle has sides of lengths 8 cm and 10 cm, with an included angle of 45 degrees. Use the law of sines to find the length of the third side.

• 6.50 cm

• 9.00 cm

• 7.07 cm

• 8.50 cm

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

• 25 m

• 15 m

• 35 m