Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 43^{\circ}$, the opposite side to the angle is $9.2$ and the adjacent side is $x$. So, $\tan43^{\circ}=\frac{9.2}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{9.2}{\tan43^{\circ}}$. Since $\tan43^{\circ}\approx0.9325$, then $x = \frac{9.2}{0.9325}$.

Step3: Calculate the value of $x$

$x=\frac{9.2}{0.9325}\approx9.9$.

Answer:

$9.9$