Question

what is m∠j to the nearest tenth?
3.4
15.1
o 31.9
o 38.5
o 52.5
58.1

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle $JLK$ with right - angle at $L$, we know the adjacent side to $\angle J$ is $JL = 9.4$ and the opposite side is $LK=15.1$. We use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan J=\frac{LK}{JL}$.

Step2: Calculate the tangent value

Substitute the given values: $\tan J=\frac{15.1}{9.4}\approx1.6064$.

Step3: Find the angle

To find $\angle J$, we take the inverse tangent (arctan) of the value we just calculated. So, $J = \arctan(1.6064)$. Using a calculator, $J\approx58.1^{\circ}$.

Answer:

$58.1$