Question

question express cos k as a fraction in simplest terms.

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle K$, the adjacent side to $\angle K$ is $KJ = 6$, and we need to find the hypotenuse $KI$.

Step2: Use the Pythagorean theorem

In right - triangle $KIJ$ with legs $KJ = 6$ and $IJ = 8$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. So, $KI=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$.

Step3: Calculate $\cos K$

$\cos K=\frac{KJ}{KI}$. Substituting $KJ = 6$ and $KI = 10$, we get $\cos K=\frac{6}{10}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$