Question

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

Explanation:

Step1: Identify trigonometric relation

Since we have a right - triangle with an angle and the adjacent side to the angle, and we want to find the opposite side, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute values

Here, $\theta = 68^{\circ}$ and the adjacent side $a = 5$, and the opposite side is $x$. So, $\tan(68^{\circ})=\frac{x}{5}$.

Step3: Solve for x

Multiply both sides by 5: $x = 5\times\tan(68^{\circ})$.
We know that $\tan(68^{\circ})\approx2.475$, so $x=5\times2.475 = 12.375$.

Step4: Round to the nearest tenth

Rounding 12.375 to the nearest tenth gives $x\approx12.4$.

Answer:

$12.4$