Question

Finding an Unknown Side

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

Short answer

The value is$\mathit{x}\mathbf{=}\mathbf{31}\mathbf{.303}$

Step-by-step solution

Step 1. Given information

A triangle with known value of a side of 25 and an angle of${53}^{\circ }$

Step 2. Concept used

There is a side and an angle that is well-known. Use trigonometric equations to discover unknown sides. Use formulae as-

Where

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

Step 3. Calculation

From given figure,

$\begin{array}{l}\Rightarrow \theta ={53}^{°}\\ \Rightarrow p=25\\ \Rightarrow h=x\end{array}$

Now use the formulae,

$\begin{array}{l}\sin \theta =\frac{p}{h}\\ \Rightarrow \sin 53=\frac{25}{x}\\ \Rightarrow 0.7986355=\frac{25}{x}\\ \Rightarrow x=\frac{25}{0.7986355}\\ \Rightarrow x=31.3033914\\ \Rightarrow x\approx 31.303\end{array}$