Question

Marc is building a gazebo and wants to brace each corner by placing an 8-inch wooden bracket diagonally. How far below the corner should he fasten the bracket if he wants the distances from the corner to each end of the bracket to be equal? (Round to the nearest tenth of an inch.)

Options:
a) 4.0 inches
b) 5.7 inches
c) 8.0 inches
d) 11.3 inches

Answer 1

Marc should fasten the bracket approximately 5.7 inches below the corner.

Step-by-step explanation:

To find the distance below the corner where Marc should fasten the bracket, we need to use the Pythagorean theorem. Let's assume the distance from the corner to each end of the bracket is x inches. This forms a right triangle with one leg as x inches, another leg as x inches, and the hypotenuse as 8 inches. Using the Pythagorean theorem, we can write:

x^2 + x^2 = 8^2

2x^2 = 64

x^2 = 32

x = sqrt(32)

x ≈ 5.7 inches

Therefore, Marc should fasten the bracket approximately 5.7 inches below the corner.