Question

Use the rules of Special right triangles to find x and y: 8) 45° 2V2 V X = [ Select] > [ Select] 4 y= 272 4/2

Answer 1

We could use the mathematical identity

$\begin{gathered} \frac{2\sqrt[]{2}}{x}=\cos 45 \\ \frac{2\sqrt[]{2}}{x}=\frac{\sqrt[]{2}}{2} \\ \text{cross multiply} \\ 4\sqrt[]{2}=x\sqrt[]{2} \\ \text{divide both sides by }\sqrt[]{2} \\ x=4 \end{gathered}$

To find y, we use

$\begin{gathered} \frac{y}{2\sqrt[]{2}}=\tan 45 \\ \frac{y}{2\sqrt[]{2}}=1 \\ \text{cross multiply} \\ y=2\sqrt[]{2} \end{gathered}$

This is to be expected since the triangle is isosceles.

Therefore, we have;

$\begin{gathered} x=4 \\ y=2\sqrt[]{2} \end{gathered}$