Question

solve for x.
x = (round to the nearest hundredth.)

Explanation:

Step1: Identify the trigonometric relation

In right - triangle ABC, we know the adjacent side to the angle of 34° is 42 and we want to find the opposite side x. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(34^{\circ})=\frac{x}{42}$.

Step2: Solve for x

Multiply both sides of the equation $\tan(34^{\circ})=\frac{x}{42}$ by 42. We get $x = 42\times\tan(34^{\circ})$.
Since $\tan(34^{\circ})\approx0.6745$, then $x = 42\times0.6745=28.329$.

Step3: Round the result

Rounding 28.329 to the nearest hundredth gives $x\approx28.33$.

Answer:

$28.33$