Question

Solve for the missing side lengths.45°5A. O57057666, yB.O57224,357245,122 -2, y522D. x = 5/2, y = 5/2

Answer 1

The missing sides, x, and y can be obtained using the sine rule

Step 1: Get the angle at A

The angle at A is obtained below:

$180-90-45=45^0$

Step 2: Use the sine rule

$\frac{\sin A}{y}=\frac{\sin B}{x}=\frac{\sin C}{5}$

$\begin{gathered} \text{where A=45}^0 \\ B\text{=45}^0 \\ C=90^0 \end{gathered}$

To get y

$\frac{\sin45}{y}=\frac{\sin 90}{5}$

cross multiply

$y=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}$

To get x

$\frac{\sin45}{x}=\frac{\sin 90}{5}$$x=\frac{5\times\sin 45}{\sin 90}=\frac{5\sqrt[]{2}}{2}$

Therefore, the answer is option C