Question

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

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle B\), the adjacent side is \(BC = 32\) and the hypotenuse is \(AB=68\).

Step2: Calculate \(\cos(B)\)

\(\cos(B)=\frac{32}{68}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 32 and 68 is 4. So, \(\frac{32\div4}{68\div4}=\frac{8}{17}\).

Answer:

\(\frac{8}{17}\)