Question

Finding an Unknown Side

Find the side labeled. State your answer rounded to five decimal places.

Short answer

The value is$\mathit{x}\mathbf{=}\mathbf{11}\mathbf{.25833}$

Step-by-step solution

Step 1. Given information

A triangle with known value of a side of 13 and an angle of ${60}^{°}$

Step 2. Concept used

There is a known side and one known angle. For finding unknown side, use trigonometric formulae. Use formulae as-

Where

$\begin{array}{l}h=hypotenuse\\ b=base\\ p=perpendicular\end{array}$

Step 3. Calculation

From given figure,

$\begin{array}{l}\Rightarrow \theta ={60}^{°}\\ \Rightarrow h=13\\ \Rightarrow p=x\end{array}$

Now use the formulae,

$\begin{array}{l}\sin \theta =\frac{p}{h}\\ \Rightarrow \sin 60=\frac{x}{13}\\ \Rightarrow 0.8660254=\frac{x}{13}\\ \Rightarrow x=0.8660254\times 13\\ \Rightarrow x=11.2583302\\ \Rightarrow x\approx 11.25833\end{array}$