Question

Find the Value oftge variables. if the answer is not an integer leave it in simplest form

Answer 1

In order to obtain the value for x, we will make use of the trigonometric functions SOHCAHTOA.

Given:

$\begin{gathered} \theta=60^0 \\ \text{Opposite}=x \\ \text{Hypotenuse}=8 \end{gathered}$

The trigonometric function that relates both the opposite and hypotenuse is SOH (Sine of angles).

$\begin{gathered} \sin 60^0=\frac{x}{8} \\ \therefore x=8\sin 60^0=8\times\frac{\sqrt[]{3}}{2}=4\sqrt[]{3} \end{gathered}$

Hence,

$x=4\sqrt[]{3}$