Question

Find the exact value of x in the figure. 30° 36 450

Answer 1

The triangle is,

Using trigonometric equations for right triangle ACB,

`\begin{gathered} \cos 30^(\circ)=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos 30^(\circ)=(y)/(36) \\ 36*\cos 30^(\circ)=y \\ 36*\frac{\sqrt[]{3}}{2}=y \\ 18\sqrt[]{3}=y \end{gathered}`

Using trigonometric equations for right triangle ACD,

`\begin{gathered} \tan 45^(\circ)=\frac{\text{opposite side}}{adjacent\text{ side}} \\ \tan 45^(\circ)=(y)/(x) \\ x=(y)/(\tan45^(\circ)) \\ x=\frac{18\sqrt[]{3}}{1} \\ x=18\sqrt[]{3} \\ \text{Therefore, the value of x is }18\sqrt[]{3} \end{gathered}`