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

Question

Responses

36
36

38
38

37
37

39

Answer 1

To find the angle of elevation \(\theta\) formed by the ramp, we can use the inverse sine function. The sine of the angle is equal to the ratio of the opposite side (the height difference between the two levels) to the hypotenuse (the length of the ramp).

Using the information provided:

• The height difference (opposite side) is \(2.5\) feet.
• The length of the ramp (hypotenuse) is \(4\) feet.

We can express this relationship as follows:

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

Now, we calculate \(\frac{2.5}{4}\):

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

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

\[ \theta = \sin^{-1}(0.625) \]

Using a calculator, we find:

\[ \theta \approx 38.68 \]

Rounding to the nearest whole degree, we get:

\[ \theta \approx 39 \]

Thus, the approximate angle of elevation formed by the ramp is:

39 degrees.