find ik. write your answer as an integer or as a decimal rounded to the nearest tenth. ik =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle $IKJ$, we know the angle $\angle J = 61^{\circ}$ and the adjacent side to $\angle J$ is $IJ = 3.9$, and we want to find the opposite side $IK$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. $\tan J=\frac{IK}{IJ}$

Step2: Substitute the values

We know that $J = 61^{\circ}$ and $IJ = 3.9$. So $\tan61^{\circ}=\frac{IK}{3.9}$. Since $\tan61^{\circ}\approx1.804$, we have $IK = 3.9\times\tan61^{\circ}$. $IK=3.9\times1.804$

Step3: Calculate the value

$IK = 3.9\times1.804 = 7.0356$. Rounding to the nearest tenth, we get $IK\approx7.0$.

Answer:

$7.0$