Question

solve for x. round to the nearest tenth, if necessary. answer attempt 1 out of 2 x =

Explanation:

Step1: Identify trigonometric relation

In right - triangle TUV, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 40^{\circ}$, the opposite side to $\angle T$ is $x$ and the adjacent side is 64. So, $\tan40^{\circ}=\frac{x}{64}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan40^{\circ}=\frac{x}{64}$ by 64. We know that $\tan40^{\circ}\approx0.8391$. Then $x = 64\times\tan40^{\circ}$. So, $x=64\times0.8391 = 53.7024$.

Step3: Round to nearest tenth

Rounding 53.7024 to the nearest tenth gives 53.7.

Answer:

53.7