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: 78.85 ftStep-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: [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] By definition: [tex]\alpha+108\°=180\°[/tex] Then, this is: [tex]\alpha=180\°-108\°\\\alpha =72\°[/tex] In the right triangle shown in the figure, you can identify: [tex]opposite=75\\hypotenuse=x[/tex] Then, you need to substitute the corresponding values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:  [tex]sin(72\°)=\frac{75}{x}[/tex] Now, you can solve for "x": [tex]xsin(72\°)=75\\\\x=\frac{75}{sin(72\°)}\\\\x=78.85\ ft[/tex]