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°

37°
37°

53°

Answer 1

To find the angle formed where the metal piece rests on the wall, we can use the properties of a right triangle and the inverse sine function.

In this scenario, we can denote:

• The opposite side (the height the shelf comes out from the wall) as 1 foot.
• The hypotenuse (the diagonal distance of the metal piece) as 1.25 feet.

Using the sine function:

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

Substituting the known values:

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

Now, to find the angle \(\theta\), we take the inverse sine (arcsin) of 0.8:

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

Using a calculator:

\[ \theta \approx 53.13° \]

Hence, the angle formed where the metal piece rests on the wall is approximately:

53°

The correct response is 53°.