Question

express cos r as a fraction in simplest terms. answer attempt 1 out of 3 cos r = submit answer

Explanation:

Step1: Find the length of side \(RS\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) in right - triangle \(RST\), where \(c = RT = 7\), \(a=\sqrt{12}\), and \(b = RS\).

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Step2: Use the cosine formula

The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle R\), the adjacent side is \(RS\) and the hypotenuse is \(RT\).
\(\cos R=\frac{RS}{RT}\)

Since \(RS = \sqrt{37}\) and \(RT = 7\), \(\cos R=\frac{\sqrt{37}}{7}\)

Answer:

\(\frac{\sqrt{37}}{7}\)