Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 64^{
∘. How tall is the tree if the point on the ground is 49 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary

Answer 1

The height of the tree that forms an angle of 64 degrees and point from the tree is 49 feet is 100.46 ft

The situation forms a right angle triangle.

How to find the sides when given angle of elevation

using trigonometric ratios,

tan 64 = opposite / adjacent

Where

• opposite side = height of the tree
• adjacent side = distance from the point on the ground from the tree.

Therefore,

tan 64 = h / 49

cross multiply

h = 49 × tan 64

h = 49 × 2.05030384158

h = 100.464888237

h = 100.46 ft

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