You are to construct a decorative wood shelf that has two metal angle supports that fasten to the bottom of the shelf and resemble a right triangle. The shelves are to stick out from the wall 1 foot, and the diagonal distance of the metal piece is 1.25 feet. Using the inverse of sine, what is the approximate angle formed where the metal piece rests on the wall?(1 point)

Question

Responses

53°
53°

90°
90°

61°
61°

37°

Answer 1

To find the angle formed where the metal piece rests on the wall, we can use the sine function based on the right triangle formed by the shelf.

In this scenario, the shelf sticks out 1 foot horizontally from the wall (the opposite side) and the diagonal distance (the hypotenuse) is 1.25 feet. We can use the sine function:

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

Substituting the known values:

\[ \sin(\theta) = \frac{1 \text{ foot}}{1.25 \text{ feet}} \]

Calculating:

\[ \sin(\theta) = \frac{1}{1.25} = 0.8 \]

Next, we find \(\theta\) by taking the inverse sine (arcsin) of 0.8:

\[ \theta = \arcsin(0.8) \]

Using a calculator, we find:

\[ \theta \approx 53° \]

Therefore, the approximate angle formed where the metal piece rests on the wall is:

53°