Question

express cos a as a fraction in simplest terms.
answer attempt 1 out of 2
cos a =

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}\). First, find the hypotenuse \(AC\) using the Pythagorean theorem \(AC=\sqrt{AB^{2}+BC^{2}}\). Given \(AB = \sqrt{91}\) and \(BC=\sqrt{78}\), then \(AC=\sqrt{(\sqrt{91})^{2}+(\sqrt{78})^{2}}=\sqrt{91 + 78}=\sqrt{169}=13\).

Step2: Calculate \(\cos A\)

The adjacent side to angle \(A\) is \(AB=\sqrt{91}\), and the hypotenuse \(AC = 13\). So \(\cos A=\frac{AB}{AC}=\frac{\sqrt{91}}{13}\).

Answer:

\(\frac{\sqrt{91}}{13}\)