Question

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

Explanation:

Step1: Recall the cosine formula

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

Step2: Identify adjacent and hypotenuse

For \(\angle A\), the adjacent side is \(AC\). Use the Pythagorean theorem \(AC=\sqrt{AB^{2}-BC^{2}}\). Given \(AB = 17\) and \(BC=15\), then \(AC=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}=\sqrt{32\times2}=\sqrt{64}=8\). The hypotenuse \(AB = 17\).

Step3: Calculate \(\cos(A)\)

\(\cos(A)=\frac{AC}{AB}=\frac{8}{17}\)

Answer:

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