Mastering Triangle Properties with the Law of Sines

A triangle has two sides measuring 8 cm and 10 cm, and the angle opposite the 10 cm side is 30 degrees. Find the angle opposite the 8 cm side using the law of sines.

• 60 degrees

• 45 degrees

• 15 degrees

• 23.58 degrees

In a triangle, one angle measures 45 degrees, and the side opposite this angle is 12 m. If another side measures 15 m, find the angle opposite the 15 m side.

• 30.0 degrees

• 61.0 degrees

• 75.0 degrees

• 90.0 degrees

A boat sails from point A to point B, creating a triangle with point C. If angle A is 50 degrees, angle B is 70 degrees, and side AC is 100 m, calculate the length of side AB using the law of sines.

• 105.00 m

• 130.75 m

• 90.25 m

• 116.56 m

A surveyor measures a triangle where angle A is 60 degrees, angle B is 50 degrees, and side a (opposite angle A) is 200 m. Determine the length of side b using the law of sines.

• 200 m

• 150 m

• 180 m

• 171.88 m

In a triangle, angle C is 90 degrees, side a is 5 m, and side b is 12 m. Use the law of sines to find angle A.

• 15 degrees

• 30 degrees

• 22.62 degrees

• 45 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 ft long, find the height the ladder reaches on the wall.

• 9.66 ft

• 7.2 ft

• 10.5 ft

• 8.5 ft

A triangular park has one angle measuring 30 degrees and the side opposite this angle is 50 m. If another side measures 70 m, find the angle opposite the 70 m side using the law of sines.

• 60.000°

• 44.427°

• 75.000°

• 30.000°

In a triangle, angle A is 40 degrees, side a is 25 m, and side b is 30 m. Calculate angle B using the law of sines.

• 50.5 degrees

• 30 degrees

• 70 degrees

• 60 degrees

A triangle has sides measuring 7 m, 9 m, and an angle of 45 degrees opposite the 9 m side. Use the law of sines to find the remaining angles of the triangle.

• Angle A: 36.87 degrees, Angle C: 98.13 degrees

• Angle A: 50 degrees, Angle C: 80 degrees

• Angle A: 30 degrees, Angle C: 120 degrees

• Angle A: 45 degrees, Angle C: 90 degrees

A pilot is flying from point X to point Y, creating a triangle with point Z. If angle X is 30 degrees, angle Y is 60 degrees, and side XY is 200 km, find the distance from point X to point Z using the law of sines.

• 173.21 km

• 200 km

• 180 km

• 150 km