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?
To find the angle formed by the metal piece where it rests on the wall, we can use the inverse sine function. The inverse sine function, also known as arcsine, provides the angle whose sine is a given value.
In this case, we want to find the angle whose sine is the ratio of the opposite side (1 foot) to the hypotenuse (1.25 feet).
sin(angle) = opposite/hypotenuse
sin(angle) = 1/1.25
angle = arcsin(1/1.25)
Using a calculator, we can find the approximate value of the inverse sine:
angle ≈ arcsin(0.8) ≈ 53.13 degrees
Therefore, the approximate angle formed where the metal piece rests on the wall is 53.13 degrees.