Question

find the cosine of ∠k. simplify your answer and write it as a proper fraction, improper fraction, or whole number. cos(k) =

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle K$

Adjacent side to $\angle K$: $KJ = 6$; Opposite side: $JI = 8$

Step3: Calculate hypotenuse $KI$

Use Pythagorean theorem: $KI = \sqrt{KJ^2 + JI^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$

Step4: Compute $\cos(K)$

Substitute values into cosine formula: $\cos(K) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{6}{10} = \frac{3}{5}$

Answer:

$\frac{3}{5}$