Tangent Triumphs: Solving Real-World Elevation Problems

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

• 10 feet

• 5√3 feet

A ramp is built to help wheelchair access. If the ramp rises 4 feet over a horizontal distance of 12 feet, what is the angle of elevation of the ramp?

• 30 degrees

• 25 degrees

• 18.43 degrees

• 15 degrees

A ladder leans against a wall, forming a 60-degree angle with the ground. If the base of the ladder is 5 feet away from the wall, how tall is the ladder?

• 6.5 feet

• 7.2 feet

• 8.66 feet

• 10 feet

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?

• 75 meters

• 50 meters

• 120 meters

• 100 meters

A kite is flying at an angle of 40 degrees with the ground. If the string of the kite is 50 meters long, how high is the kite above the ground?

• 25 meters

• 50 meters

• 32.14 meters

• 40 meters

A person is standing 30 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 50 degrees, how tall is the flagpole?

• 25 meters

• 35.75 meters

• 40 meters

• 50 meters

A boat is anchored 20 meters from the shore. If the angle of elevation from the boat to the top of a lighthouse is 70 degrees, how tall is the lighthouse?

• 54.94 meters

• 70 meters

• 45 meters

• 30 meters

A construction worker is looking at a crane that is 25 meters away. If the angle of elevation to the top of the crane is 35 degrees, how tall is the crane?

• 22 meters

• 30 meters

• 17.5 meters

• 10 meters

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

• 17.32 meters

• 10 meters

• 15 meters

• 20 meters

A cyclist is riding up a hill that has a 15-degree incline. If the cyclist travels 100 meters up the hill, how much vertical distance have they gained?

• 50.00 meters

• 25.88 meters

• 30.00 meters

• 10.00 meters