Question

Finding an Unknown Side Find rounded to one decimal place.

Short answer

The value of xfrom the given triangle is 63.7.

Step-by-step solution

Step 1. Given information. 

The angles of triangle are ${50}^{\circ }$, ${65}^{\circ }$.

Step 2. Finding the value of y

Substituting the known values of $\theta ={60}^{°}$and the opposite side 50 in the above trigonometric ratio formulae, we get,

$\begin{array}{l}\sin {60}^{°}=\frac{50}{y}\\ \Rightarrow \frac{\sqrt{3}}{2}=\frac{50}{y}\\ \Rightarrow y=\frac{100}{\sqrt{3}}\\ \Rightarrow y=57.74\end{array}$

Step3. Finding the value of x

Now, substituting the values of y, 65in the second right-angled triangle, we get,

$\begin{array}{c}\sin {65}^{°}=\frac{y}{x}\\ \Rightarrow 0.9063=\frac{57.74}{x}\\ \Rightarrow x=\frac{57.74}{0.9063}\\ \Rightarrow x=63.71\end{array}$

Rounding off x the obtained value to one decimal place, we get,$x=63.7$