Question #162486

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?


1
Expert's answer
2021-02-16T12:37:27-0500

Solution.

By the sine theorem,

xsin30°=45sin60°,\frac{x}{\sin30°}=\frac{45}{\sin60°}, from here


x=451232=453=25.98feet.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=31.9825.98+6=31.98 feet, where 31.98<4031.98<40 feet.

Answer. 31.98feet.31.98\, \text{feet}.

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