Question

A ramp 18 ft long rises to a platform that is 16 ft off the ground. Find x, the angle of elevation of the ramp. Round youranswer to the nearest tent of a degree.

Answer 1

SOLUTION

The triangle is a right angle triangle with the following parameters given in the diagram

$\begin{gathered} \text{angle of elevation,}\theta=x \\ \text{Hypotenuses =18ft} \\ \text{opposite side=16ft} \end{gathered}$

Using the trigonometry ratio for the sine of an angle, we have

$\sin \theta=\frac{opposite}{hypotenuse}$

Then we substituting the parameters into the formula above, we obtain

$\begin{gathered} \sin x=\frac{16}{18} \\ \sin x=\frac{8}{9} \\ \sin x=0.8889 \end{gathered}$

Then the value of x becomes

$\begin{gathered} x=\sin ^{-1}(0.8889) \\ x=62.7^0 \end{gathered}$

Therefore x= 62.7°