Question

find the cosine of $\angle j$. simplify your answer and write it as a proper fraction, improper fraction, or whole number. $\cos(j) = \square$

Explanation:

Step1: Identify right triangle sides

For $\angle J$, adjacent side $KJ=16$, opposite side $IK=30$.

Step2: Calculate hypotenuse $IJ$

Use Pythagorean theorem:
$$IJ = \sqrt{IK^2 + KJ^2} = \sqrt{30^2 + 16^2} = \sqrt{900 + 256} = \sqrt{1156} = 34$$

Step3: Apply cosine definition

Cosine = adjacent/hypotenuse:
$$\cos(J) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{16}{34}$$

Step4: Simplify the fraction

Divide numerator/denominator by 2:
$$\cos(J) = \frac{8}{17}$$

Answer:

$\frac{8}{17}$