Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In this right - triangle, $\theta = 24^{\circ}$, the adjacent side to the angle $24^{\circ}$ is 6 and the opposite side is $x$. So, $\tan(24^{\circ})=\frac{x}{6}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(24^{\circ})=\frac{x}{6}$ by 6. We get $x = 6\times\tan(24^{\circ})$.
Since $\tan(24^{\circ})\approx0.4452$, then $x=6\times0.4452 = 2.6712$.

Step3: Round the answer

Rounding $2.6712$ to the nearest tenth gives $x\approx2.7$.

Answer:

$2.7$