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 sine function, which relates the opposite side to the hypotenuse in a right triangle. The formula is:

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

In this case, the opposite side is the difference in height between the two levels (2.5 feet), and the hypotenuse is the length of the ramp (4 feet):

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

Calculating the ratio:

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

Next, we use the inverse sine function (arcsin) to find the angle \(\theta\):

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

Using a calculator, we find:

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

Rounding to the nearest whole degree, we get:

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

Thus, the angle of elevation formed by the ramp is approximately 39 degrees.