Question

The wind has blown a tree so that it is growing at a 108° angle with the ground. The top of the tree is 75 ft. from the ground. How tall is the tree?

Answer 1

Answer: 78.85 ft

Step-by-step explanation:

 Based on the information provided in the exercise, you can draw the right triangle attached, wheree "x" is the height of the tree.

You need to remember the following identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

By definition:

$\alpha+108\°=180\°$

Then, this is:

$\alpha=180\°-108\°\\\alpha =72\°$

In the right triangle shown in the figure, you can identify:

$opposite=75\\hypotenuse=x$

Then, you need to substitute the corresponding values into  $sin\alpha=\frac{opposite}{hypotenuse}$:

 $sin(72\°)=\frac{75}{x}$

Now, you can solve for "x":

$xsin(72\°)=75\\\\x=\frac{75}{sin(72\°)}\\\\x=78.85\ ft$