Question

Finding an Unknown Side

Find the side labeled $\mathit{x}$.

Short answer

The value is$\mathit{x}\mathbf{=}\mathbf{16}\mathbf{.517}$

Step-by-step solution

Step 1. Given information

A triangle with known value of a side of 12 and an angle of${36}^{\circ }$

Step 2. Concept used

A side and an angle are both known. Use trigonometric formulas to get the unknown side. Use formulae as-

$\begin{array}{l}\Rightarrow \sin \theta =\frac{p}{h}\\ \Rightarrow \cos \theta =\frac{b}{h}\\ \Rightarrow \tan \theta =\frac{p}{b}\end{array}$

Where

Step 3. Calculation

From given figure,

$\begin{array}{l}\Rightarrow \theta ={36}^{°}\\ \Rightarrow b=x\\ \Rightarrow p=12\end{array}$

Now use the formulae,

$\begin{array}{l}\tan \theta =\frac{p}{b}\\ \Rightarrow \tan 36=\frac{12}{x}\\ \Rightarrow 0.7265425=\frac{12}{x}\\ \Rightarrow x=\frac{12}{0.7265425}\\ \Rightarrow x=16.5165830\\ \Rightarrow x\approx 16.517\end{array}$