Question

Finding an Unknown Side

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

Short answer

The value is$\mathit{x}\mathbf{=}\mathbf{12}\mathbf{.5}$

Step-by-step solution

Step 1. Given information

A triangle with the known value of a side of 25 and an angle of $30°$

Step 2. Concept used

In this question, use the trigonometric identities of angles. 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

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

Step 3. Calculation

From the given figure,

$\begin{array}{l}\Rightarrow \theta ={30}^{°}\\ \Rightarrow h=25\\ \Rightarrow p=x\end{array}$

Now use the formulae,

$\begin{array}{l}\sin \theta =\frac{p}{h}\\ \Rightarrow \sin 30=\frac{x}{25}\\ \Rightarrow 0.500=\frac{x}{25}\\ \Rightarrow 0.5\times 25=x\\ \Rightarrow x=12.5\end{array}$