GCEMathematicsTrigonometry2023

In triangle PQR, PQ = 8 cm, QR = 6 cm and angle PQR = 120°. Find PR, correct to the nearest whole number. [Use the cosine rule]

A12 cmCORRECT
B10 cm
C14 cm
D7 cm
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Why the answer is A, and why the others tempt you.
By the cosine rule: PR² = PQ² + QR² - 2(PQ)(QR)cos(120°) = 64 + 36 - 2(8)(6)(-1/2) = 100 + 48 = 148. Therefore PR = √148 ≈ 12.17 ≈ 12 cm. Option B (10) results from ignoring the cosine term, and option C (14) comes from adding instead of correctly applying the sign of cos 120°.
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