Finding Side Lengths Using the Law of Sines

A triangle has angles A = 30° and B = 45°. If side a = 10 cm, find the length of side b using the law of sines.

• 10√2 cm

• 5 cm

• 15 cm

• 20 cm

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle ABC, angle A = 50° and angle B = 60°. If side a = 12 m, calculate the length of side b.

• 14.0 m

• 10.5 m

• 16.2 m

• 12.5 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A boat sails from point A to point B, creating a triangle with angle A = 70° and angle B = 40°. If the distance from A to C (the point directly across from B) is 15 km, find the distance from A to B.

• 25.30 km

• 30.00 km

• 18.50 km

• 21.92 km

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle XYZ, angle X = 35° and angle Y = 75°. If side x = 20 m, use the law of sines to find the length of side y.

• 25.50 m

• 40.20 m

• 30.75 m

• 34.64 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A surveyor measures angle A = 55° and angle B = 85° in triangle ABC. If side a = 25 ft, determine the length of side b.

• 28 ft

• 40 ft

• 20 ft

• 32.5 ft

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A triangular park has angles measuring 45°, 60°, and 75°. If the side opposite the 45° angle is 30 m, find the lengths of the other two sides.

• b ≈ 36.74 m, c ≈ 41.00 m

• b ≈ 40.00 m, c ≈ 50.00 m

• b ≈ 30.00 m, c ≈ 45.00 m

• b ≈ 25.00 m, c ≈ 35.00 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In triangle DEF, angle D = 40° and angle E = 70°. If side d = 18 cm, calculate the length of side e using the law of sines.

• 18.75 cm

• 26.28 cm

• 22.15 cm

• 30.50 cm

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A ladder leans against a wall forming a triangle with the ground. If the angle between the ladder and the ground is 60° and the distance from the wall to the base of the ladder is 5 m, find the length of the ladder.

• 12 m

• 10 m

• 8 m

• 15 m

Tags

CCSS.HSG.SRT.C.8

In triangle PQR, angle P = 30° and angle Q = 50°. If side p = 10 m, find the length of side q using the law of sines.

• 12.50 m

• 18.75 m

• 15.32 m

• 20.00 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

A triangle has angles measuring 30°, 60°, and 90°. If the side opposite the 30° angle is 5 m, find the lengths of the other two sides.

• 5 m and 15 m

• The lengths of the other two sides are 5√3 m and 10 m.

• 10√2 m and 5 m

• 7 m and 12 m

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11