Real-Life Applications of Sine & Cosine: Angles & Sides

A tree casts a shadow of 15 meters. If the angle of elevation from the tip of the shadow to the top of the tree is 30 degrees, how tall is the tree?

• 7 meters

• 5√3 meters (approximately 8.66 meters)

• 12√2 meters (approximately 16.97 meters)

• 10 meters

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

• 8 cm

• 10√(3/2) cm

• 15√2 cm

• 12 cm

A boat is sailing from point A to point B, which is 100 meters away. If the angle between the boat's current position and the line to point B is 50 degrees, how far is the boat from point A?

• 50 meters

• 64.28 meters

• 90 meters

• 80 meters

In triangle XYZ, angle X is 70 degrees, angle Y is 50 degrees, and side x is 12 cm. Calculate the length of side y using the law of sines.

• 9.14 cm

• 10.50 cm

• 8.25 cm

• 11.00 cm

A ladder leans against a wall, forming a 75-degree angle with the ground. If the foot of the ladder is 4 meters from the wall, how long is the ladder?

• 12.5 meters

• 18 meters

• 10 meters

• 15.5 meters

In triangle DEF, angle D is 30 degrees, angle E is 45 degrees, and side d is 8 cm. Find the length of side e using the law of sines.

• 8√2 cm

• 10 cm

• 7√3 cm

• 6 cm

A surveyor measures a triangle with angles of 40 degrees and 70 degrees. If the side opposite the 40-degree angle is 50 meters, what is the length of the side opposite the 70-degree angle?

• 80.25 meters

• 70.71 meters

• 60.50 meters

• 90.00 meters

A kite is flying at an angle of 60 degrees from the ground. If the string of the kite is 20 meters long, how high is the kite above the ground?

• 10 meters

• 15 meters

• 25 meters

• 17.32 meters

In triangle GHI, angle G is 80 degrees, side g is 15 cm, and side h is 10 cm. Find angle H using the law of cosines.

• 50 degrees

• 30 degrees

• 40 degrees

• 70 degrees

A triangular park has sides measuring 30 meters, 40 meters, and 50 meters. Calculate the angle opposite the longest side using the law of cosines.

• 90 degrees

• 120 degrees

• 60 degrees

• 45 degrees