Real-World Applications of Tangent in Trigonometry

A tree casts a shadow that is 15 meters 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 meters

• 5 meters

• 8.66 meters

• 12 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 10 meters long, how high does the ramp rise?

• 3.42 meters

• 5.0 meters

• 4.8 meters

• 2.5 meters

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

• 18.40 meters

• 10.25 meters

• 15.59 meters

• 12.75 meters

A surveyor is standing 50 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, how tall is the building?

• 30 meters

• 100 meters

• 50 meters

• 70 meters

A kite is flying at an angle of 60 degrees from the ground. If the string of the kite is 30 meters long, how high is the kite above the ground?

• 30 meters

• 20 meters

• 15 meters

• 25.98 meters

A person is standing 25 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 35 degrees, what is the height of the flagpole?

• 10 meters

• 17.5 meters

• 25 meters

• 30 meters

A boat is anchored 100 meters from the shore. If the angle of elevation from the boat to the top of a cliff is 40 degrees, how high is the cliff?

• 100.0 meters

• 84.0 meters

• 70.0 meters

• 60.0 meters

A construction worker is using a crane that makes a 50-degree angle with the ground. If the crane's arm is 12 meters long, how high can the worker lift an object?

• 9.19 meters

• 7.5 meters

• 11.0 meters

• 10.2 meters

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 distance have they covered?

• 100 meters

• 30 meters

• 51.76 meters

• 75 meters

A photographer is standing 30 meters away from a statue. If the angle of elevation to the top of the statue is 25 degrees, how tall is the statue?

• 20.3 meters

• 10.5 meters

• 15.2 meters

• 13.99 meters