Question

I NEED HELP IN UNDER 10 MINUTES, just tell me the X

Answer 1

Given the triangle ΔABC as shown below:

Required: value of x.

Step 1:

Using 30° as the focus angle, label the sides of the triangle.

Thus,

`\begin{gathered} AB\Rightarrow hypotenuse \\ AC\Rightarrow adjacent \\ BC\Rightarrow opposite \end{gathered}`

Step 2:

Evaluate the length x

`\begin{gathered} \tan \text{ 30 = }(opposite)/(adjacent) \\ \tan \text{ 30 = }(BC)/(AC) \\ \text{but tan 30 = }(√(3))/(3) \\ \text{thus,} \\ \frac{\sqrt[]{3}}{3}\text{ = }\frac{\sqrt[]{2}}{x} \\ x*\sqrt[]{3}\text{ = }\sqrt[]{2}\text{ }*\text{ 3} \\ \Rightarrow x\text{ = }\frac{3\sqrt[]{2}\text{ }}{\sqrt[]{3}}\text{ } \end{gathered}`

Step 3:

Rationalize the denominator.

Thus,

`\begin{gathered} \text{ }\frac{3\sqrt[]{2}\text{ }}{\sqrt[]{3}}\text{ }*\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ =\frac{3\sqrt[]{2}\text{ }*\sqrt[]{3}}{3} \\ =\frac{3\sqrt[]{6}\text{ }}{3} \\ \text{Thus, } \\ x=\sqrt[]{6}\text{ } \end{gathered}`

Hence, the lenth of