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# What's this angle of elevation given two others? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7756

## Question

The angular elevation of the summit of a mountain is measured from three points on a straight level road. From a point due south of the summit the elevation is $\alpha$, from a point due east of it the elevation is $\beta$, and from the point of the road nearest to the summit the elevation is $\gamma$.

If the direction of the road makes angle $\theta$ east of north, prove that

1. $\tan\theta=\tan\alpha\cot\beta$

2. $\tan^2\gamma=\tan^2\alpha+\tan^2\beta$.

Find $\gamma$, if $\theta=31^{\circ}$ and $\alpha=8^{\circ}$.
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