Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In this right - triangle, $\theta = 49^{\circ}$, the opposite side to the angle $\theta$ is 26 m and the adjacent side is $x$. So, $\tan49^{\circ}=\frac{26}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{26}{\tan49^{\circ}}$. Since $\tan49^{\circ}\approx1.150368$, then $x=\frac{26}{1.150368}$.

Step3: Calculate the value of $x$

$x=\frac{26}{1.150368}\approx22.6$.

Answer:

$22.6$