aclynn 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) ≈ ≈ °

1 answer

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

Let:

  • \( h = 2.5 \) feet (the height difference)
  • \( L = 4 \) feet (the length of the ramp)

The sine of the angle \( \theta \) can be calculated using the formula:

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

Substituting the values:

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

Now calculating the value:

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

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

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

Using a calculator:

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

Rounding to the nearest whole degree gives us:

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

Therefore, the approximate angle of elevation formed by the ramp is 39°.