Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 54∘ . How tall is the tree if the point on the ground is 89 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

122.50 feet

Explanation:

First, recall
`\tan(\theta)=((opp)/(adj))`, where opp is the leg of the right triangle representing the height of the tree and adj represents the leg of the right triangle representing the distance from the tree. For this problem, let

Θ= 54°

adj = 89 ft.

So,

`\tan(54^o)=((opp)/(89ft))\\1.376=((opp)/(89ft))\\(1.376)(89ft)=((opp)/(89ft))(89ft)\\122.498ft=opp`

For this problem, remember the opposite side represents the height of the tree. So, the height of the tree, rounded to the nearest hundredth, is 122.50 feet.