Question

Renee is building a gazebo and wants to brace each corner by placing a 22 inch wooden bracket diagonally as shown. 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 ?

Answer 1

EXPLANATION

If he wants that the distance from the corner to each end of the bracket would be equal, the angle should be of 45 degrees.

So, if the angle is of 45 degrees we can apply the Pythagorean Theorem to find the value of x as shown as follows.

`\sin 45=\frac{opposite\text{ cathetus }}{\text{hypotenuse}}=(x)/(22)`

Multiplying both sides by 22:

`22\cdot\sin 45=\text{x}`

Solving the argument:

`22\cdot\frac{\sqrt[]{2}}{2}=x`

Simplifying:

`11\cdot\sqrt[]{2}=x`

Switching sides:

`x=11\sqrt[]{2}=15.5inches`

The bracket should be 15.5 inches far way.