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Melissa is standing 40 ft from a tree. The angle of elevation from where she is standing on the ground to the top of the tree is 50°.

How tall is the tree?



Round the final answer to the nearest tenth.

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Respuesta :

Tan(angle) = opposite length/ adjacent length

Tan(50) = h/40
h = 40 x tan(50)
h = 47.67 or 47.7 feet
calculista

Answer:

[tex]47.7\ ft[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In a right triangle the tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle

so

In this problem

[tex]tan(50\°)=\frac{BC}{AC}[/tex]

The tall of the tree is BC

[tex]BC=ACtan(50\°)[/tex]

[tex]AC=40\ ft[/tex]

substitute

[tex]BC=40*tan(50\°)=47.7\ ft[/tex]

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