#### Answer

The length of the brace is 10.6 feet

#### Work Step by Step

Let angle $B = 115^{\circ}$
Let angle $C = 22^{\circ}$
Let angle $A$ be the angle of the triangle between the brace and the wall. We can find angle $A$:
$A+B+C = 180^{\circ}$
$A = 180^{\circ}-B-C$
$A = 180^{\circ}-115^{\circ}-22^{\circ}$
$A = 43^{\circ}$
We can use the law of sines to find the length of the brace $b$:
$\frac{b}{sin~B} = \frac{8.0~ft}{sin~A}$
$b = \frac{8.0~ft~sin~B}{sin~A}$
$b = \frac{(8.0~ft)~sin~(115^{\circ})}{sin~43^{\circ}}$
$b = 10.6~ft$
The length of the brace is 10.6 feet