Question

Please help me solve for X, I am including a picture

Answer 1

x = 14

Step-by-step explanation:

To get the value of x, we wll be using the SOH CAH TOA identity

Using sin theta = opposite/hypotenuse

`\begin{gathered} sin45\text{ = }\frac{h}{7\sqrt[]{6}} \\ h\text{ =7}\sqrt[]{6}\text{ sin45} \\ h\text{ = 7}\sqrt[]{6}*\frac{1}{\sqrt[]{2}} \\ h\text{ = 7}\sqrt[]{3} \end{gathered}`

h is the vertical height of the triangles.

Next is to get the value of x;

Similarly;

`\begin{gathered} \sin \text{ 60 = }(h)/(x) \\ \text{ sin60 = }\frac{7\sqrt[]{3}}{x} \\ x\text{ = }\frac{7\sqrt[]{3}}{\sin 60} \\ x\text{ = }\frac{7\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ x\text{ = 7}\sqrt[]{3}*\frac{2}{\sqrt[]{3}} \\ x\text{ = 7}\cdot2 \\ x\text{ =14} \end{gathered}`

Hence the value of x required is 14