Question

I've been stuck on this one and I can't figure out x y or b

Answer 1

Determine the length of x by using trigonometry in smaller triangle.

`\begin{gathered} \sin 60=(x)/(4) \\ \frac{\sqrt[]{3}}{2}=(x)/(4) \\ x=2\sqrt[]{3} \end{gathered}`

Consider the larger triangle.

Determine the length of side b by using trigonometry.

`\begin{gathered} \tan 60=(b)/(4) \\ \sqrt[]{3}=(b)/(4) \\ b=4\sqrt[]{3} \end{gathered}`

Consider the upper right angle triangle.

Determine the length of side y by using the trigonometric ratio.

`\begin{gathered} \text{tan}30=(x)/(y) \\ \frac{1}{\sqrt[]{3}}=\frac{2\sqrt[]{3}}{y} \\ y=2\sqrt[]{3}\cdot\sqrt[]{3} \\ =2\cdot3 \\ =6 \end{gathered}`