Question

I need to find side x in its simplest radical form using the special right triangles method

Answer 1

Answer:

\sqrt{6}

Explanation:

From the given diagram,

Hypotenuse sde = x

Opposite side = \sqrt{3}

Using the SOH CAH TOA identity

Sintheta = opposite/hypotenuse

Sin 45 = \sqrt{3}/x

x = \sqrt{3}/sin45

$\begin{gathered} x\text{ =}\frac{\sqrt[]{3}}{\sin 45} \\ x\text{ = }\frac{\sqrt[]{3}}{\frac{1}{\sqrt[]{2}}} \\ x\text{ = }\sqrt[]{3^{}}\cdot\sqrt[]{2} \\ x\text{ =}\sqrt[]{6} \end{gathered}$

Hence the value of x is \sqrt{6}