A shelf that is 27 cm wide is held up by a triangular bracket. The bracket makes a 42.1° angle with the bottom of the shelf. What is the height of the bracket?
a. 18.69 cm
c. 18.1 cm
b. 20.03 cm
d. 24.4 cm
To find the height of the bracket, we can use the sine function since we have the angle and the width of the shelf. The sine function relates the opposite side (height in this case) to the hypotenuse (width of the shelf).
The formula for the sine function is:
sin(angle) = opposite/hypotenuse
We can rearrange the equation to solve for the opposite side (height):
opposite = sin(angle) * hypotenuse
Angle = 42.1°
Hypotenuse (width of the shelf) = 27 cm
Using the given values, we can calculate the height of the bracket:
opposite = sin(42.1°) * 27 cm
opposite = 0.6691 * 27 cm
opposite ≈ 18.08 cm
Therefore, the height of the bracket is approximately 18.08 cm.
The closest answer choice is:
c. 18.1 cm