Question

The angle of elevation to a nearby tree from a point on the ground is measured to be 45^{\circ} ∘ . How tall is the tree if the point on the ground is 79 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

Answer: 79 ft

Explanation:

Given

The angle of elevation is
`45^(\circ)`

Distance of the point from the tree is
`79\ ft`

Suppose h is the height of the tree.

`\Rightarrow (h)/(79)=\tan 45^(\circ)\\\\\Rightarrow h=79\tan 45^(\circ)\quad [\tan 45^(\circ)=1]\\\Rightarrow h=79\ ft`

Thus, the height of the tree is 79 ft