Question

An observer, whose eyes are 1.98 m above the ground, is standing 39.2 m away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer's line of sight with the treetop makes an angle of 20.9° above the horizontal. How tall is the tree?

Answer 1

Answer:

The tree is 16.25 m tall.

Explanation:

Attached is a diagram that better explains the problem.

From the diagram we see that the distance between the top of the tree and the line of sight of the observer is x.

To find the height of the tree, we need to first find x and then add it to the height of the observers line of sight from the ground.

Using SOHCAHTOA trigonometric function:

tan(20) = x/39.2

=> x = 39.2 * tan(20)

x = 39.2 * 0.364

x = 14.27m

Hence, the height of the tree is:

(14.27 + 1.98)m

16.25m

The tree is 16.25 m tall.