find jk. write your answer as an integer or as a decimal rounded to the nearest tenth. jk =
find jk. write your answer as an integer or as a decimal rounded to the nearest tenth. jk =
Answer
Explanation:
Step1: Identify the trigonometric relation
In right - triangle $JKI$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 68^{\circ}$, the opposite side to $\angle J$ is $IK=\sqrt{66}$, and the adjacent side is $JK$. So, $\tan68^{\circ}=\frac{IK}{JK}$.
Step2: Rearrange the formula to solve for $JK$
We know that $\tan68^{\circ}\approx2.475$, and $IK = \sqrt{66}\approx8.124$. From $\tan68^{\circ}=\frac{IK}{JK}$, we can get $JK=\frac{IK}{\tan68^{\circ}}$. Substitute the values: $JK=\frac{\sqrt{66}}{\tan68^{\circ}}\approx\frac{8.124}{2.475}\approx3.3$.
Answer:
$3.3$