Question

Jaclynn is building a cat house for her cats. She designs a ramp from one level to the other for them to climb. The ramp length is 4 feet, and the difference between the two levels is 2.5 feet. Using the inverse of sine function, what is the approximate angle of elevation formed by the ramp? Round your answer to the nearest whole degree.(1 point) ≈ °

Answer 1

To find the angle of elevation formed by the ramp, we can use the inverse sine function (arcsin).

First, we define the components of the situation:
- The length of the ramp is the hypotenuse of a right triangle, which is 4 feet.
- The height difference between the two levels (opposite side) is 2.5 feet.

Using the definition of the sine function in a right triangle, we have:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{2.5}{4}
\]

Now, we calculate:

\[
\sin(\theta) = \frac{2.5}{4} = 0.625
\]

Next, we use the inverse sine function to find the angle:

\[
\theta = \arcsin(0.625)
\]

Using a calculator to find the inverse sine:

\[
\theta \approx 38.68^\circ
\]

Rounding this to the nearest whole degree gives:

\[
\theta \approx 39^\circ
\]

Thus, the approximate angle of elevation formed by the ramp is \(\boxed{39}\) degrees.