Question

I need help finding the missing length with a radical form as an answer! I will provide the full photo

Answer 1

By Trigonometric Ratio,

`\begin{gathered} \tan 60=(2)/(y) \\ \text{Cross multiply to get,} \\ y=(2)/(\tan 60) \\ y=\frac{2}{\sqrt[]{3}} \\ y=\frac{2\text{ }\sqrt[]{3}}{\sqrt[]{3}\text{ }*\sqrt[]{3}} \\ y=\frac{2\sqrt[]{3}}{3} \\ y=(2)/(3)\text{ }\sqrt[]{3} \end{gathered}`

To find the value of x :

`\begin{gathered} \sin 60=(2)/(x) \\ \text{Cross multiplying, we get,} \\ x=(2)/(\sin 60) \\ \\ x=\frac{2}{\frac{\sqrt[]{3}}{2}}=\frac{4}{\sqrt[]{3}} \\ \\ x=\frac{4\sqrt[]{3}}{\sqrt[]{3}*\sqrt[]{3}} \\ \\ x=\frac{4\text{ }\sqrt[]{3}}{3} \end{gathered}`