Question

express cos m as a fraction in simplest terms.

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle M\), the adjacent side to \(\angle M\) is \(ML\) and the hypotenuse is \(MK\).

Step2: Substitute the values

We know that \(ML = 9\) and \(MK=15\). So, \(\cos M=\frac{ML}{MK}\).

Step3: Simplify the fraction

\(\cos M=\frac{9}{15}=\frac{9\div3}{15\div3}\) (dividing numerator and denominator by their greatest common divisor, which is 3).

Answer:

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