Question

I'm confused about how to solve this using the special right triangles method

Answer 1

`x=4\sqrt[]{2}`

Explanation:

We can calculate the value of x, by means of the trigonometric function sine

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{opposite = }4 \\ \theta\text{ =60\degree} \\ \text{hypotenuse = x} \end{gathered}`

Replacing:

`\begin{gathered} \sin 45=(4)/(x) \\ x=(4)/(\sin45) \\ \sin 45=\frac{\sqrt[]{2}}{2} \\ x=\frac{4}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ x=\frac{8\sqrt[]{2}}{2} \\ x=4\sqrt[]{2} \end{gathered}`