Question

24.5 m
x
67°
58°

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third - angle be $y$. So $y=180-(67 + 58)=55^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we have $\frac{x}{\sin67^{\circ}}=\frac{24.5}{\sin55^{\circ}}$.

Step3: Solve for $x$

Cross - multiply to get $x=\frac{24.5\times\sin67^{\circ}}{\sin55^{\circ}}$.
We know that $\sin67^{\circ}\approx0.9205$ and $\sin55^{\circ}\approx0.8192$.
$x=\frac{24.5\times0.9205}{0.8192}=\frac{22.55225}{0.8192}\approx27.53$ m.

Answer:

$x\approx27.53$ m