Omar wants to determine $cos\theta$ in a right triangle. If the length of the adjacent side to angle $\theta$ is 5 units and the hypotenuse is 13 units, what is $cos\theta$?

• A. $\frac{5}{13}$
• B. $\frac{5}{12}$
• C. $\frac{12}{13}$
• D. $\frac{13}{5}$

Answer: (A)

Verified step by step guidance

1. Recall the definition of cosine in a right triangle: \(\cos \theta = \frac{\text{length of adjacent side}}{\text{length of hypotenuse}}\).
2. Identify the given values from the problem: the adjacent side to angle \(\theta\) is 5 units, and the hypotenuse is 13 units.
3. Substitute the given values into the cosine formula: \(\cos \theta = \frac{5}{13}\).
4. Simplify the fraction if possible (in this case, \(\frac{5}{13}\) is already in simplest form).
5. Conclude that \(\cos \theta\) is the ratio of the adjacent side over the hypotenuse, which is \(\frac{5}{13}\).