Question

The roof leading to the top of a hill has an angle of elevation of 23 degrees. The hill is 120 feet high what is the leanth of the road to the top of the hill to the nearest hundredth

Answer 1

Answer: $307.11\ ft$

Step-by-step explanation:

Given

The height of hill is 120 ft and the angle of elevation is $23^{\circ}$

Suppose the length of the road is $x$

From the figure, we can write

$\Rightarrow \sin 23^{\circ}=\dfrac{120}{x}\\\\\Rightarrow x=\dfrac{120}{\sin 23^{\circ}}\\\\\Rightarrow x=307.11\ ft$

Thus, the length of the road is $307.11\ ft$