Answer to Question #162486 in Geometry for Jai

Question

joe has been hired to choose a tree for his town’s holiday celebration. he has been told by the town council that the tree cannot exceed a hight of 40 feet due to town regulations. he finds a tree, stands 45 feet away from the base, and looks up 30° from his horizontal sight line to determine its hight. If Joe is exactly 6 feet tall, what is the height of the tree, to the nearest hundredth of a foot?

Answer 1

Solution.

By the sine theorem,

$\frac{x}{\sin30°}=\frac{45}{\sin60°},$ from here

$$x=\frac{45 \cdot \frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{45}{\sqrt{3}}=25.98\, \text{feet}.$$

The height of the tree is equal to $25.98+6=31.98$ feet, where $31.98<40$ feet.

Answer. $31.98\, \text{feet}.$