Question

Please help me I don’t know how to do this

Answer 1

Recall the trigonometric function tangent.

`\tan \theta=\frac{\text{opposite}}{\text{adjacent}}`

We can use either 30° or 60° as our basis for the angle. In this case, we will use 60° (using 30° works just as well, we just have to determine its corresponding opposite and adjacent sides)

`\begin{gathered} \text{Given} \\ \theta=60\degree \\ \text{opposite to }\theta=x \\ \text{adjacent to }\theta=\sqrt[]{8} \end{gathered}`

Substitute these values to the tangent function and we have

`\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan 60\degree=\frac{x}{\sqrt[]{8}} \end{gathered}`

Multiply both sides with square root of 8, to get rid of the fraction in the right side.

`\begin{gathered} \sqrt[]{8}\cdot\tan 60\degree=\frac{x}{\sqrt[]{8}}\cdot\sqrt[]{8} \\ \sqrt[]{8}\cdot\tan 60\degree=\frac{x}{\cancel{\sqrt[]{8}}}\cdot\cancel{\sqrt[]{8}} \\ \sqrt[]{8}\cdot\tan 60\degree=x \\ \\ x=\sqrt[]{8}\cdot\tan 60\degree \end{gathered}`

Recall that tan 60° = square root of 3 therefore

`\begin{gathered} x=\sqrt[]{8}\cdot\tan 60\degree \\ x=\sqrt[]{8}\cdot\sqrt[]{3} \\ x=\sqrt[]{8\cdot3} \\ x=\sqrt[]{24} \\ x=\sqrt[]{4\cdot6} \\ x=2\sqrt[]{6} \\ \\ \text{Therefore, the value of }x\text{ is }2\sqrt[]{6} \end{gathered}`