Question

find the value of x, correct to 1 decimal place.

Explanation:

Step1: Identify the trigonometric relation

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 40^{\circ}$, the opposite side is 72 m and the adjacent side is $x$. So, $\tan40^{\circ}=\frac{72}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{72}{\tan40^{\circ}}$. Since $\tan40^{\circ}\approx0.8391$, then $x = \frac{72}{0.8391}\approx85.8$.

Answer:

$85.8$