Trigonometry: Heights & Angles in Real-Life Scenarios

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, what is the height of the tree?

• 8.66 meters

• 12 meters

• 5 meters

• 10 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 high does the ladder reach on the wall?

• 10.5 meters

• 18.3 meters

• 12.0 meters

• 14.24 meters

A ramp is built to allow wheelchair access to a building. If the ramp rises 1.5 meters over a horizontal distance of 6 meters, what is the angle of elevation of the ramp?

• 25.0 degrees

• 20.3 degrees

• 10.5 degrees

• 14.74 degrees

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?

• 50 meters

• 75 meters

• 100 meters

• 150 meters

A flagpole casts a shadow that is 20 feet long. If the angle of elevation from the tip of the shadow to the top of the flagpole is 60 degrees, what is the height of the flagpole?

• 34.64 feet

• 40 feet

• 25 feet

• 15 feet

A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 35 degrees, how high is the hill?

• 45 meters

• 25.5 meters

• 60 meters

• 35.01 meters

A construction worker needs to determine the angle of elevation to the top of a crane that is 10 meters tall and 8 meters away from the base of the crane. What is the angle of elevation?

• 51.34 degrees

• 45 degrees

• 60 degrees

• 30 degrees

A kite is flying at a height of 30 meters. If the string of the kite makes an angle of 40 degrees with the horizontal, how long is the string?

• 25.00 meters

• 46.15 meters

• 35.50 meters

• 50.00 meters

A building is 50 meters tall. If a person stands 30 meters away from the base of the building, what is the angle of elevation to the top of the building?

• 75 degrees

• 30 degrees

• 59.04 degrees

• 45 degrees

A ski slope has a vertical drop of 200 meters and a horizontal distance of 800 meters. What is the angle of descent of the slope?

• 20.3 degrees

• 10.5 degrees

• 25.0 degrees

• 14.04 degrees