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Question

Help me please and show work please From a boat on the lake, the angle of elevation to the top of a cliff is 14°28'. If the base of the cliff is 743 feet from the boat, how high is the cliff (to the nearest foot)?

Answer 1

Imagine a right triangle with a base of 743 feet and an unknown height. The angle of elevation is the angle from the ground, in other words, the angle the base makes with the hypotenuse, which is 14°28' ≈ 14.47°. Since you know one side length and an angle, you can solve for the height, using the equation

 

tan(θ) = height/base

tan(14°28') = height/743

height = 743tan(14°28')

height ≈ 192 ft