Question

express cos a as a fraction in simplest terms.

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the adjacent side and hypotenuse

For angle \(A\), the adjacent side to angle \(A\) is \(AB = 48\), and the hypotenuse \(AC=50\).

Step3: Calculate \(\cos A\)

\(\cos A=\frac{48}{50}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 48 and 50 is 2. So \(\frac{48\div2}{50\div2}=\frac{24}{25}\).

Answer:

\(\frac{24}{25}\)