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

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent - side to the given angle and we want to find the opposite - side. We use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute the values

Given $\theta = 44^{\circ}$ and the adjacent side $a = 17$, and the opposite side is $x$. So $\tan(44^{\circ})=\frac{x}{17}$.

Step3: Solve for $x$

Multiply both sides of the equation by 17: $x = 17\times\tan(44^{\circ})$. We know that $\tan(44^{\circ})\approx0.9657$. Then $x=17\times0.9657 = 16.4169$.

Step4: Round the answer

Rounding $16.4169$ to the nearest tenth gives $x\approx16.4$.

Answer:

$16.4$