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°) = [tex] \frac{Height}{Base} \;=\;\frac{h}{55} [/tex]
[tex] 0.6745\;=\;\frac{h}{55} [/tex]
h = 55 × 0.6745 = 37.0979 feet
So, height of the tree = 37.1 feet.
