Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 52
∘
∘
. How tall is the tree if the point on the ground is 82 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

The elevation and the top of the tree form a right triangle

The height of the tree is 104.96 feet

How to determine the height of the tree?

The given parameters are:

• Angle of elevation = 52 degrees
• Horizontal distance (b) = 82 feet

The height (h) of the tree is calculated using the following trigonometry ratio

tan(α) = h/b

Make h the subject

h = b * tan(α)

Substitute known values

h = 82* tan(52)

Evaluate the product

h = 104.96

Hence, the height of the tree is 104.96 feet

Read more about right triangles at:

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