Question

find the cosine of \\( \angle c \\).
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\( \cos ( c ) = \\)

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle C\), the adjacent side to \(\angle C\) is \(DC = 24\), and the hypotenuse is \(BC=74\).

Step2: Calculate \(\cos(C)\)

Using the formula \(\cos(C)=\frac{DC}{BC}\), substitute \(DC = 24\) and \(BC = 74\) into the formula. So \(\cos(C)=\frac{24}{74}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 24 and 74 is 2. \(\frac{24\div2}{74\div2}=\frac{12}{37}\).

Answer:

\(\frac{12}{37}\)