Question

When i stand 30 feet away from a tree at home, the angle of elevation to the top of the tree is 50◦ and the angle of depression to the base of the tree is 10◦ . What is the height of the tree? Round your answer to the nearest foot?

Answer 1

1. You can use the information given in the problem above to draw the diagram of the situation, as you can see in the figure attached.
2. You must calculate the heights $h1$ and $h2$ and sum them to find the total height $Ht$ of the tree, as below:

$Tan(50)=\frac{h1}{30} \\ h1=35.75ft$

$Tan(10)=\frac{h2}{30} \\ h2=5.28ft$

$Ht=h1+h2\\ Ht=41 ft$

The answer is: $41 ft$