Applying Tangent: Real-World Height Problems for 10th Grade

A tree casts a shadow that is 15 feet long. 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?

• 10 feet

• 12 feet

• 5√3 feet

• 7 feet

A ramp is built to help wheelchair access to a building. If the ramp makes a 20-degree angle with the ground and is 10 feet long, how high does the ramp reach?

• 2.5 feet

• 4.8 feet

• 3.42 feet

• 5.0 feet

A ladder is leaning against a wall. If the foot of the ladder is 4 feet away from the wall and the angle between the ladder and the ground is 60 degrees, how tall is the wall?

• 5 feet

• 4√3 feet (approximately 6.93 feet)

• 8 feet

• 3 feet

A surveyor is standing 50 meters away from a building and measures the angle of elevation to the top of the building as 45 degrees. How tall is the building?

• 70 meters

• 50 meters

• 100 meters

• 30 meters

A kite is flying at an angle of 40 degrees from the ground. If the string of the kite is 30 meters long, how high is the kite above the ground?

• 25.0 meters

• 22.1 meters

• 19.28 meters

• 15.5 meters

A person is standing 25 meters away from a flagpole and measures the angle of elevation to the top of the flagpole as 35 degrees. What is the height of the flagpole?

• 22.75 meters

• 17.51 meters

• 30.00 meters

• 10.25 meters

A boat is anchored 100 meters from a dock. If the angle of elevation from the boat to the top of the dock is 25 degrees, how high is the dock?

• 55 meters

• 70 meters

• 46.63 meters

• 30 meters

A construction worker is using a crane that is 50 feet tall. If the angle of elevation from the ground to the top of the crane is 70 degrees, how far is the worker from the base of the crane?

• 25 feet

• 17.5 feet

• 10 feet

• 30 feet

A photographer is standing 30 feet away from a statue and looks up at an angle of 50 degrees to capture the photo. How tall is the statue?

• 25 feet

• 50 feet

• 35.75 feet

• 40 feet

A cyclist is riding up a hill that has a 15-degree incline. If the cyclist travels 200 meters up the hill, how much vertical height has the cyclist gained?

• 75 meters

• 51.76 meters

• 100 meters

• 30 meters