Question

The upper part of a tree, broken by wind, makes an angle of 38º with the ground. the horizontal distance from the root of the tree to the point where the top of the tree meets the ground is 20 meters. find the height of the tree before it was broken.

Answer 1

After the tree is broken, it makes a right angle triangle with horizontal leg being 20 m and making 38° with the hypotenuse.
The height of the tree before it broke constitutes the sum of upright leg and the hypotenuse.

Using sine rules,
tan 38 = Upright leg/Horizontal leg => Upright leg = Horizontal leg * tan 38 = 20*tan 38 = 15.63 m
Additionally,
Hypotenuse = Sqrt (Upright leg^2 + Horizontal leg^2) = Sqrt (15.63^2+20^2) = 25.38 m

Therefore,
Height of before it broke = 15.63 + 25.38 = 41.01 m