Question

Solve for the missing side lengths.45°5A.2566, y5706B52Cy524C5122y522U5V2, y = 5V2

Answer 1

To calculate x, we will use the trigonometry ratio

`\begin{gathered} \sin \theta=(opposite)/(hypotenus) \\ \text{where,} \\ \text{opposite =opp=x} \\ \text{hypotenus}=\text{hyp}=5 \end{gathered}`

Therefore,

`\begin{gathered} \sin 45^0=(x)/(5) \\ x=5* sin45^0 \\ x=5*\frac{\sqrt[]{2}}{2} \\ x=\frac{5\sqrt[]{2}}{2} \end{gathered}`

To calculate y, we will use the trigonometric ratio,

`\begin{gathered} \cos \theta=(adjacent)/(hypotenus) \\ \text{where,} \\ \text{adjacent}=\text{adj}=y \\ \text{hypotenus}=\text{hyp}=5 \\ \end{gathered}`

Therefore,

`\begin{gathered} \cos 45^0=(y)/(5) \\ y=5*\cos 45^0 \\ y=5*\frac{\sqrt[]{2}}{2} \\ y=\frac{5\sqrt[]{2}}{2} \end{gathered}`

Hence,

The correct answer is OPTION C