Given the right triangle below, evaluate $\(\cos\]\theta\)$.

• A. $\(\cos\]\theta\)=\(\frac{8}{17}\)$
• B. $\(\cos\]\theta\)=\(\frac{8}{15}\)$
• C. $\(\cos\]\theta\)=\(\frac{15}{17}\)$
• D. $\(\cos\]\theta\)=\(\frac{15}{8}\)$

Answer: (C)

Verified step by step guidance

1. Identify the sides of the right triangle: the side adjacent to angle θ is 15, the opposite side is 8, and the hypotenuse is 17.
2. Recall the definition of cosine for a right triangle: cos(θ) = adjacent/hypotenuse.
3. Substitute the known values into the cosine formula: cos(θ) = 15/17.
4. Verify the calculation by checking the Pythagorean theorem: 15^2 + 8^2 = 17^2, which confirms the side lengths are correct.
5. Conclude that the correct value of cos(θ) is 15/17.