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

90°
90°

61°
61°

53°
53°

37°

Answer 1

To find the angle formed where the metal piece rests on the wall, we can use the sine function. In this context, we can identify the right triangle formed by the shelf, the wall, and the metal support.

Given:

• The horizontal distance from the wall to the end of the shelf (opposite side) = 1 foot
• The diagonal distance of the metal piece (hypotenuse) = 1.25 feet

We want to find the angle \( \theta \) at the wall, which can be calculated by:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{1.25} \]

Now, calculating the sine:

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

Next, we find \( \theta \) using the inverse sine function:

\[ \theta = \sin^{-1}(0.8) \]

Using a calculator or trigonometric tables, we can find \( \theta \):

\[ \theta \approx 53.13^\circ \]

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

53°

So, the correct response would be: 53°