In right triangle $JKL$, if $cos\left(K\right)$ = $\frac{24}{51}$, what is the length of the side adjacent to angle $K$ if the hypotenuse is $51$?

• A. $24$
• B. $48$
• C. $51$
• D. $27$

Answer: (A)

Verified step by step guidance

1. Recall the definition of cosine in a right triangle: \(\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}\).
2. Identify the given values: \(\cos(K) = \frac{24}{51}\) and the hypotenuse length is 51.
3. Set up the equation using the cosine definition: \(\cos(K) = \frac{\text{adjacent side}}{51} = \frac{24}{51}\).
4. To find the length of the side adjacent to angle \(K\), multiply both sides of the equation by 51: \(\text{adjacent side} = 51 \times \frac{24}{51}\).
5. Simplify the expression to find the length of the adjacent side.