Question

Finding an Unknown Side Find rounded to one decimal place.

Short answer

The value of xfrom the given triangle is 98.2.

Step-by-step solution

Step 1. Given information.

The angles of the right angle triangle are ${85}^{\circ }$, ${30}^{\circ }$.

Step 2. Finding the value of y

Assuming an unknown dimension in the right-angled triangle as y as shown in the figure.

Substituting the known values of $\theta ={60}^{°}$and 85 as the opposite side in the above trigonometric ratio formulae, we get,

$\begin{array}{c}\tan {60}^{°}=\frac{85}{y}\\ \Rightarrow y=\frac{85}{\left(\sqrt{3}\right)}\\ \Rightarrow y=49.07\end{array}$

Step 3. Finding the value of x

Now, considering the complete right-angled triangle KLM, we get,

$\begin{array}{c}\tan {30}^{°}=\frac{85}{x+y}\\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{85}{x+49.07}\\ \Rightarrow x=(85*\sqrt{3})-49.07\\ \Rightarrow x=98.154\end{array}$

Rounding off x to one decimal place, we get,$x=98.2$