Calculating Side Lengths with the Law of Sines

A triangle has one angle measuring 30 degrees and a side opposite to it measuring 10 meters. Calculate the length of the side opposite to the 60-degree angle.

• 10√3 meters

• 5 meters

• 20√2 meters

• 15 meters

In a triangle, angle A is 45 degrees, angle B is 75 degrees, and side a (opposite angle A) is 12 cm. Find the length of side b (opposite angle B).

• 15.00 cm

• 12.73 cm

• 10.50 cm

• 9.80 cm

A boat is sailing 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 (from A to C) is 15 meters, how long is side b (from B to C)?

• 12.50 meters

• 18.36 meters

• 20.00 meters

• 15.75 meters

A surveyor measures a triangle where angle A is 40 degrees, angle B is 60 degrees, and side a is 25 meters. Calculate the length of side b.

• 33.69 meters

• 25.00 meters

• 40.00 meters

• 20.50 meters

In a triangle, angle C is 90 degrees, angle A is 30 degrees, and side a (opposite angle A) is 20 meters. Use the law of sines to find the length of side c (the hypotenuse).

• 40 meters

• 30 meters

• 25 meters

• 50 meters

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 foot of the ladder is 3 meters from the wall, how long is the ladder?

• 10.00 meters

• 12.50 meters

• 9.81 meters

• 11.62 meters

A triangular park has one angle measuring 45 degrees and the side opposite to it measuring 50 meters. If the angle adjacent to this side is 60 degrees, find the length of the other side.

• 55.25 meters

• 70.50 meters

• 58.31 meters

• 45.00 meters

In a triangle, angle A is 30 degrees, angle B is 45 degrees, and side a is 10 meters. Calculate the length of side b using the law of sines.

• 10√2 meters

• 15 meters

• 20√3 meters

• 5 meters

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 meters long, how high is the kite above the ground?

• 25 meters

• 43.3 meters

• 60 meters

• 30 meters

A triangular field has angles measuring 30 degrees, 60 degrees, and 90 degrees. If the side opposite the 30-degree angle is 40 meters, find the lengths of the other two sides using the law of sines.

• 30 meters and 60 meters

• The lengths of the other two sides are 40√3 meters and 80 meters.

• 50 meters and 70 meters

• 20√3 meters and 60 meters