Question

Finding an Unknown Side Find rounded to one decimal place.

Short answer

The value of xfrom the given triangle is 5.8

Step-by-step solution

Step 1. Given information.

The angles of the triangle is${30}^{\circ }$

Step 2. Finding the value of angle TRS

Considering the figure, we get,

$\angle QRT={60}^{°}$since the sum of the angles in a triangle is${180}^{\circ }$.

Therefore, we get, $\angle TRS={30}^{°}$

Step 3. Finding the value of x

Substituting the known values of ${30}^{°}$and the adjacent side 5 of the lower triangle $\Delta RTS$in the above trigonometric ratio formulae, we get,

$\begin{array}{l}\cos {30}^{°}=\frac{5}{x}\\ \Rightarrow \frac{\sqrt{3}}{2}=\frac{5}{x}\\ \Rightarrow x=\frac{10}{\sqrt{3}}\\ \Rightarrow x=5.7735\end{array}$

Rounding the value of xoff to one digit, we get$x=5.8$