Question

You and your group have decided that the height of the eye of the panther must be 3.6 metres above the gym floor. You measure the angle of elevation from the gym floor to the eye of the panther as being 36.87◦. Find the distance from the boundary line to the bleacher (known as floor clearance) to the nearest tenth of a metre.

Answer 1

6 meters

Explanation

to solve this we need to use a trigonometric function

Step 1

a) here we have a right triangle, so let

$\begin{gathered} hypotenuse\text{ = x} \\ angle=36.87 \\ opposite\text{ side=3.6} \end{gathered}$

hence we need a function that relates those values, it is

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

Step 2

finally, replace and solve for x( hypotenuse)

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ 36.87=}\frac{3.6}{x} \\ x=\frac{3.6}{sin36.87} \\ x=5.99 \\ rounded\text{ } \\ x=6 \end{gathered}$

therefore, the answer is 6 meters

I hope this helps you