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

`(\sin A)/(y)=(\sin B)/(x)=(\sin C)/(5)`

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

To get y

`(\sin45)/(y)=(\sin 90)/(5)`

cross multiply

`y=(5*\sin 45)/(\sin 90)=\frac{5\sqrt[]{2}}{2}`

To get x

`(\sin45)/(x)=(\sin 90)/(5)`
`x=(5*\sin 45)/(\sin 90)=\frac{5\sqrt[]{2}}{2}`

Therefore, the answer is option C