Sine & Cosine: Real-Life Applications in Geometry

A tree casts a shadow of 15 feet. 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 feet

• 12 feet

• 5√3 feet

• 10 feet

A ladder is leaning against a wall. The foot of the ladder is 4 feet away from the wall, and the ladder makes a 60-degree angle with the ground. How long is the ladder?

• 10 feet

• 8 feet

• 6 feet

• 12 feet

A ramp is built to allow wheelchair access. If the ramp rises 3 feet over a horizontal distance of 12 feet, what angle does the ramp make with the ground?

• 14.04 degrees

• 25.0 degrees

• 20.3 degrees

• 10.5 degrees

A kite is flying at a height of 20 meters. If the string makes a 45-degree angle with the ground, how long is the string?

• 25 meters

• 15 meters

• 20 meters

• 20√2 meters

A building is 50 meters tall. From a point on the ground, the angle of elevation to the top of the building is 37 degrees. How far is the point from the base of the building?

• 75 meters

• 66.4 meters

• 50 meters

• 100 meters

A surveyor is measuring a hill. If the angle of elevation to the top of the hill is 25 degrees and the distance from the surveyor to the base of the hill is 40 meters, how tall is the hill?

• 22.50 meters

• 30.00 meters

• 15.20 meters

• 18.65 meters

A person is standing 10 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 60 degrees, how tall is the flagpole?

• 10 meters

• 20 meters

• 15 meters

• 17.32 meters

A boat is anchored 30 meters from the shore. If the angle of elevation from the boat to the top of a lighthouse is 50 degrees, how tall is the lighthouse?

• 25.5 meters

• 35.754 meters

• 50 meters

• 40 meters

A construction worker is looking at a crane that is 15 meters away. If the angle of elevation to the top of the crane is 70 degrees, how tall is the crane?

• 39.5 meters

• 30 meters

• 50 meters

• 25 meters

A cyclist is riding up a hill that rises 5 meters over a distance of 20 meters. What angle does the hill make with the horizontal ground?

• 10.5 degrees

• 20 degrees

• 25 degrees

• 14.04 degrees