Question

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

Explanation:

Step1: Identify trigonometric ratio

We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 42^{\circ}$, the opposite - side to the angle is $x$ and the adjacent - side is 9. So $\tan(42^{\circ})=\frac{x}{9}$.

Step2: Solve for x

Multiply both sides of the equation $\tan(42^{\circ})=\frac{x}{9}$ by 9. We get $x = 9\times\tan(42^{\circ})$.
We know that $\tan(42^{\circ})\approx0.9004$. Then $x=9\times0.9004 = 8.1036$.

Step3: Round the answer

Rounding $8.1036$ to the nearest tenth gives $x\approx8.1$.

Answer:

$8.1$