Mastering Angles and Real-World Triangles with Sines

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

• 80 degrees

• 90 degrees

• 100 degrees

In triangle ABC, angle A measures 45 degrees, and side a (opposite angle A) is 10 cm. If side b (opposite angle B) is 15 cm, find angle B using the law of sines.

• Approximately 90.0 degrees

• Approximately 30.0 degrees

• Approximately 75.0 degrees

• Approximately 60.0 degrees

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 C is 80 degrees, and side a (from A to C) is 200 meters, how long is side b (from B to C)?

• 200 meters

• 300 meters

• 250 meters

• 150 meters

In a triangle, angle A is 60 degrees, and side a is 12 m. If side b is 15 m, calculate angle B using the law of sines.

• approximately 30 degrees

• approximately 90 degrees

• approximately 54.74 degrees

• approximately 75 degrees

A surveyor measures angle A as 35 degrees and angle B as 55 degrees in triangle ABC. If side a is 100 m, find the length of side b using the law of sines.

• 120.5 m

• 160.0 m

• 143.3 m

• 130.2 m

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 height it reaches on the wall is 10 m, find the length of the ladder using the law of sines.

• 9.5 m

• 10.58 m

• 12.3 m

• 8.7 m

In triangle DEF, angle D is 40 degrees, angle E is 70 degrees, and side d (opposite angle D) is 8 m. Find angle F and side e using the law of sines.

• Angle F: 70 degrees, Side e: 10.5 m

• Angle F: 80 degrees, Side e: 11 m

• Angle F: 60 degrees, Side e: 12 m

• Angle F: 50 degrees, Side e: 9 m

A kite is flying at an angle of elevation of 60 degrees from a point on the ground. If the string of the kite is 50 m long, what is the height of the kite above the ground?

• 25 m

• 43.3 m

• 30 m

• 50 m

In triangle GHI, angle G is 30 degrees, side g is 20 m, and side h is 25 m. Calculate angle H using the law of sines.

• 45 degrees

• 60 degrees

• 38.68 degrees

• 25 degrees

A triangular park has one angle measuring 45 degrees and the side opposite that angle measuring 30 m. If the side opposite the 60-degree angle is needed for a fence, find its length using the law of sines.

• 15√6 m

• 30√2 m

• 25√3 m

• 20 m