Question

Michael is constructing a boat ramp. He knows that the angle of elevation of the ramp is 30°. If the distance from the bottom of the boat ramp to the top of the boat ramp is 40 feet, what is the height of the boat ramp?

Answer 1

Let's draw a rough figure:

Here, h is the distance we are solving for.

Now,

With respect to the given angle 30 degrees, we have the hypotenuse and want to find the opposite side.

The trig ratio relating opposite side and hypotenuse is SINE.

Thus, we can write:

`\sin (30)=\frac{opposite}{\text{hypotenuse}}=(h)/(40)`

Cross multiiplying, we solve for h [remember, value of sin(30) is 1/2]:

`\begin{gathered} \sin (30)=(h)/(40) \\ h=40*\sin (30) \\ h=40*(1)/(2) \\ h=20 \end{gathered}`

The height of the boat ramp is 20 feet.