Estimating Heights and Distances with Angles of Elevation

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, estimate the height of the tree using a diagram.

• 8.66 meters

• 5 meters

• 10 meters

• 12 meters

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CCSS.HSG.SRT.C.8

A building is 50 meters tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. Draw a diagram and calculate the distance from the building to the point on the ground.

• 30 meters

• 100 meters

• 50 meters

• 70 meters

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CCSS.HSG.SRT.C.8

A kite is flying at an angle of elevation of 60 degrees. If the string of the kite is 20 meters long, estimate the height of the kite above the ground using a diagram.

• 15 meters

• 10 meters

• 25 meters

• 17.32 meters

Tags

CCSS.HSG.SRT.C.8

A person stands 30 meters away from a hill. If the angle of elevation to the top of the hill is 35 degrees, estimate the height of the hill. Include a diagram to support your answer.

• 15 meters

• 30 meters

• 10 meters

• 21 meters

Tags

CCSS.HSG.SRT.C.8

From the top of a lighthouse, the angle of elevation to a boat on the water is 25 degrees. If the lighthouse is 40 meters tall, estimate how far the boat is from the base of the lighthouse using a diagram.

• Approximately 50 meters

• Approximately 100 meters

• Approximately 85.7 meters

• Approximately 70 meters

Tags

CCSS.HSG.SRT.C.8

A camera is mounted on a pole that is 10 meters tall. If the angle of elevation to a bird in the sky is 70 degrees, estimate the height of the bird above the ground. Use a diagram to visualize the problem.

• Height of the bird = 10 + d * sin(70) meters

• Height of the bird = 10 + d * tan(70) meters, where d is the horizontal distance from the pole to the bird.

• Height of the bird = 10 - d * tan(70) meters

• Height of the bird = 10 + d * cos(70) meters

Tags

CCSS.HSG.SRT.C.8

A ramp is built to connect a loading dock that is 1.5 meters high. If the angle of elevation of the ramp is 20 degrees, estimate the length of the ramp. Draw a diagram to illustrate your calculations.

• 3.2 meters

• 5.0 meters

• 4.4 meters

• 6.1 meters

Tags

CCSS.HSG.SRT.C.8

A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 40 degrees, estimate the height of the statue using a diagram for visualization.

• 42 meters

• 25 meters

• 30 meters

• 55 meters

Tags

CCSS.HSG.SRT.C.8

A mountain is observed from a distance of 200 meters. If the angle of elevation to the peak of the mountain is 15 degrees, estimate the height of the mountain. Include a diagram to help visualize the scenario.

• 53.58 meters

• 30.25 meters

• 100.00 meters

• 75.10 meters

Tags

CCSS.HSG.SRT.C.8

A flagpole is 12 meters tall. From a point on the ground, the angle of elevation to the top of the flagpole is 60 degrees. Estimate the distance from the flagpole to the point on the ground using a diagram.

• 5.00 meters

• 8.50 meters

• 10.25 meters

• 6.93 meters

Tags

CCSS.HSG.SRT.C.8