Question

express cos k as a fraction in simplest terms.
right triangle with right angle at j, ji = 8, jk = 6, vertices j, i, k
answer attempt 1 out of 3
cos k = blank
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Explanation:

Step1: Identify the right triangle sides

In right triangle \( \triangle JKI \), \( \angle J = 90^\circ \), \( JK = 6 \), \( JI = 8 \). First, find the hypotenuse \( KI \) using the Pythagorean theorem: \( KI=\sqrt{JK^{2}+JI^{2}}=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100} = 10 \).

Step2: Recall the cosine definition

The cosine of an angle in a right triangle is \( \cos\theta=\frac{\text{adjacent side}}{\text{hypotenuse}} \). For \( \angle K \), the adjacent side is \( JK = 6 \), and the hypotenuse is \( KI = 10 \).

Step3: Simplify the fraction

\( \cos K=\frac{JK}{KI}=\frac{6}{10}=\frac{3}{5} \).

Answer:

\( \frac{3}{5} \)