Question

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.)

Answer 1

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.