SOHCAHTOA: Tangent Applications in Real Life Problems

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?

• 8.66 meters

• 12 meters

• 5 meters

• 10 meters

A ramp is built to allow wheelchair access to a building. If the ramp makes a 20-degree angle with the ground and is 5 meters long, how high does the ramp reach?

• 2.5 meters

• 3.0 meters

• 4.0 meters

• 1.71 meters

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

• 5 meters

• 7 meters

• 4√3 meters (approximately 6.93 meters)

• 3 meters

A surveyor is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, how tall is the building?

• 150 meters

• 100 meters

• 50 meters

• 75 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?

• 19.28 meters

• 15.5 meters

• 25.0 meters

• 22.3 meters

A person is standing 10 meters away from a flagpole. If they look up at an angle of 70 degrees to see the top of the flagpole, how tall is the flagpole?

• 35 meters

• 15 meters

• 27.47 meters

• 20 meters

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

• 28.87 meters

• 15 meters

• 45 meters

• 60 meters

A construction worker is using a crane that is 12 meters tall. If the angle of elevation from the base of the crane to the top is 45 degrees, how far is the base of the crane from the point directly below the top?

• 10 meters

• 15 meters

• 20 meters

• 12 meters

A cyclist is riding up a hill that has a slope of 15 degrees. If the cyclist travels 200 meters up the hill, how much vertical distance have they gained?

• 30 meters

• 75 meters

• 100 meters

• 51.76 meters

A photographer is standing 25 meters away from a statue. If the angle of elevation to the top of the statue is 50 degrees, how tall is the statue?

• 29.8 meters

• 35.6 meters

• 22.1 meters

• 15.2 meters