Reggie is building a bike ramp out of wood in the shape of a right triangle— the slanted portion is the ramp. He cuts a 48-inch-long wood plank that will act as the slanted portion and the base wood plank is 45 inches long. Use the inverse of cosine to find the approximate angle of the ramp from the ground.(1 point)

Question

Responses

50°
50°

90°
90°

70°
70°

20°

Answer 1

To find the angle of the ramp from the ground, we can use the cosine function, which is defined as:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

In this case, the adjacent side (the base) is 45 inches and the hypotenuse (the slanted portion of the ramp) is 48 inches.

We can rearrange the equation to solve for \(\theta\):

\[ \theta = \cos^{-1}\left(\frac{45}{48}\right) \]

Calculating \(\frac{45}{48}\):

\[ \frac{45}{48} = 0.9375 \]

Now, we find the angle using the inverse cosine:

\[ \theta = \cos^{-1}(0.9375) \]

Using a calculator, we find:

\[ \theta \approx 20.9^\circ \]

Rounding to the nearest whole number gives us approximately \(20^\circ\).

So, the answer is:

20°