Math CentralQuandaries & Queries


Question from gabby, a student:

Standing on a ledge, there is a boat 25 degrees below you. The boat has a 1,000ft. tower. If the angle of elevation to the top of the tower is 15 degrees, how high is the ledge?


Draw it out and you will see that you have two right triangles. Call the horizontal distance from you to the tower x and the height of the ledge y.

two right triangles

Can you picture it from this diagram?

tan(15) = (1000-y) / x and tan(25) = y / x.

Solve this pair of equations for y and you have your answer. Write back if you need more help.

Stephen La Rocque.

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