A boat is 100 m from the bottom of a 75 m high cliff. Calculate the angle of elevation from the...

Question:

A boat is 100 m from the bottom of a 75 m high cliff. Calculate the angle of elevation from the boat to the top of the cliff.

Tangent Function:

This function depends on the legs of a rectangular triangle, and is useful for finding information about the triangle such as internal angles. The tangent function is given by: {eq}\tan\theta=\frac{opposite}{adjacent} {/eq}

Answer and Explanation:

{eq}\begin{align*} \tan\theta&=\frac{75\:m}{100\:m} \\ \tan\theta&=\frac{3}{4} \\ \theta&=\tan^{-1}\left(\frac{3}{4}\right) \\ \theta&=36.87^{\circ} \end{align*} {/eq}


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