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.

Answer 1

To find the angle of the ramp from the ground, we can use the cosine function. In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Let's denote:

• \( A \) as the angle of the ramp from the ground,
• the length of the adjacent side (the base) as \( b = 45 \) inches,
• the length of the hypotenuse (the ramp) as \( h = 48 \) inches.

Using the cosine formula: \[ \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{h} = \frac{45}{48} \]

Now we calculate the cosine: \[ \cos(A) = \frac{45}{48} = 0.9375 \]

Next, we can find the angle \( A \) using the inverse cosine: \[ A = \cos^{-1}(0.9375) \]

Using a calculator: \[ A \approx 20.8^\circ \]

Therefore, the approximate angle of the ramp from the ground is 20.8 degrees.