Question

Juaquin is building a bike ramp with blocks and a piece of plywood. He stacks two blocks, each measuring 1 foot in height, on top of one other. He then places the plywood, which is 4 feet long, on an angle from the top of the blocks to the ground. Using the inverse of sine function, what is the angle of elevation formed where the plywood rests on the ground? Round your answer to the nearest whole degree.(1 point)

Answer 1

To determine the angle of elevation formed where the plywood rests on the ground, we can use the inverse sine function. We begin by identifying the relevant measurements:

1. The height of the stacked blocks is \( h = 2 \) feet (since each block is 1 foot high).
2. The length of the plywood is \( L = 4 \) feet.

To find the angle of elevation \( \theta \), we can model the situation using a right triangle, where:

• The opposite side (height) is the height of the blocks (2 feet).
• The hypotenuse is the length of the plywood (4 feet).

Using the sine ratio, we have:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L} = \frac{2}{4} = \frac{1}{2} \]

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

\[ \theta = \sin^{-1}\left(\frac{1}{2}\right) \]

The angle whose sine is \( \frac{1}{2} \) is \( 30^\circ \).

Thus, the angle of elevation formed where the plywood rests on the ground is:

\[ \boxed{30} \text{ degrees.} \]