Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation $\alpha =30^{o}$, $\beta=60^{o}$, respectively (Fig. A.15). The shots strike an object simultaneously at the same point. If $a=30\sqrt { 3 }\ m$ is the horizontal distance of the object from the cliff, then the height $h$ of the cliff is

Using the tangent function, the height from the bottom of the cliff to the target is a tan(beta), which is 30sqrt(3) * tan(60 deg) = 90 m. The vertical distance from the top of the cliff to the target is a tan(alpha), which is 30sqrt(3) * tan(30 deg) = 30 m. The total height h of the cliff is the sum of these two vertical distances, so h = 90 + 30 = 60 m.

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