Question

Jada is standing 10 feet away from the base of the tree and spots a nest sitting on a branch. The angle of elevation from the ground where she is standing to the nest is 55 degrees. Find the height of the nest.

Answer 1

Answer:

14.3 feet

Step-by-step explanation:

Let the height of the tree = x feet.

It is given that the horizontal distance from the base of tree = 10 feet and the angle of elevation to the nest is 55°.

So, we get the following figure.

As, we are obtaining a right angled triangle.

Using the trigonometric form for the angles of a right angled triangle, we get,

$\tan x=\frac{opposite}{adjacent}$

i.e. $\tan 55=\frac{x}{10}$

i.e. $x=10\times \tan 55$

i.e. $x=10\times 1.43$

i.e. $x=14.3$

Hence, the height of the tree is 14.3 feet.