Question

question
express \\( \cos q \\) as a fraction in simplest
terms.
answer
attempt 1 out of 3
\\( \cos q= \\)

Explanation:

Step1: Find the length of PQ

By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), in right - triangle \(OPQ\) (\(\angle P = 90^{\circ}\)), let \(PQ=x\), \(OP = \sqrt{11}\), \(OQ = 4\). Then \(x^{2}+(\sqrt{11})^{2}=4^{2}\).

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Step2: Calculate \(\cos Q\)

By the definition of cosine in a right - triangle \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle Q\), the adjacent side is \(PQ\) and the hypotenuse is \(OQ\). So \(\cos Q=\frac{PQ}{OQ}\).
Since \(PQ = \sqrt{5}\) and \(OQ = 4\), then \(\cos Q=\frac{\sqrt{5}}{4}\)

Answer:

\(\frac{\sqrt{5}}{4}\)