Question

Explanations not just answers: Sarah measures the angle of elevation to the top of a tree as 23.6 degrees from the point which is 250 m from its base. Her eye level, where the angle measurement was taken is 1.5 m above the ground. Assuming the ground to be horizontal, find the height of the tree

Answer 1

The height of the tree is h+1.5. To find hwe use a trig function that involves the side opposite the given angle and the side adjacent to the given angle, which is tangent:\[\tan \alpha=\frac{opposite}{adjacent}\]In this case, of course the side opposite is h, thus\[\tan23.6=\frac{h}{250}\]or solving for h\[h=250 \tan23.6\approx109.22\]Finall, the height of the tree is 109.2+1.5=110.7 meters.