Find the value of the angle marked x in the diagram above
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Correct Answer: Option A
Explanation:
\(PR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)cos Q\)
\(\implies cos Q = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}\)
\(\implies cos Q = \frac{8^2 + 5^2 - 7^2}{2\times8\times5}\)
\(\implies cos Q = \frac{64 + 25 - 49}{80}\)
\(\implies cos Q = \frac{40}{80} = 0.5\)
\(\implies Q = cos^{-1} (0.5) = 60^0\)
\(\therefore x = 60^0\)
\(PR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)cos Q\)
\(\implies cos Q = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}\)
\(\implies cos Q = \frac{8^2 + 5^2 - 7^2}{2\times8\times5}\)
\(\implies cos Q = \frac{64 + 25 - 49}{80}\)
\(\implies cos Q = \frac{40}{80} = 0.5\)
\(\implies Q = cos^{-1} (0.5) = 60^0\)
\(\therefore x = 60^0\)