Question

From a point 55 feet from the base of a tree, the angle from ground level to the top of the tree is 34 degrees. Find the height of the tree to the nearest foot.

Answer 1

Given the distance of a point on ground (say P) from the bae of a tree (say XY) = 55 feet.

Given the angle from ground level (point P) to the top of the tree (X) = 34°

Let's assume the height of tree (XY) = 'h' feet.

We have a Right triangle ΔXYP where ∡Y=90° and YP = 55 feet.

Using Trigonometric ratios in right triangle ΔXYP:-

Tan (34°) = $\frac{Height}{Base} \;=\;\frac{h}{55}$

$0.6745\;=\;\frac{h}{55}$

h = 55 × 0.6745 = 37.0979 feet

So, height of the tree = 37.1 feet.