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The length of a shadow of a tree is 150 feet when the angle of elevation of the sun is 39°. Approximate the height of the tree. (Round your answer to one decimal place.)

1 Answer

3 votes

Answer:

The height of tree is approximately 121.5 feet.

Explanation:

We are given following in question:

Length of shadow = 150 feet

Angle of elevation of the sun =


\theta = 39^\circ

The tree and the shadow forms a right angled triangle.

Thus, with the help of trigonometric relation, we can write:


\tan \theta = \frac{\text{Height of tree}}{\text{Length of shadow}}

Let x feet be the height of tree.

Putting all the values, we get,


\tan 39^\circ = (x)/(150)\\\\0.80978 = (x)/(150)\\\\\Rightarrow x = 150* 0.80978\\\Rightarrow x = 121.467 \approx 121.5

Thus, the height of tree is approximately 121.5 feet.

User Vijay Kumbhoje
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