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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.

Respuesta :

Answer: 79 ft

Step-by-step explanation:

Given

The angle of elevation is [tex]45^{\circ}[/tex]

Distance of the point from the tree is [tex]79\ ft[/tex]

Suppose h is the height of the tree.

[tex]\Rightarrow \dfrac{h}{79}=\tan 45^{\circ}\\\\\Rightarrow h=79\tan 45^{\circ}\quad [\tan 45^{\circ}=1]\\\Rightarrow h=79\ ft[/tex]

Thus, the height of the tree is 79 ft

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