Question

Triangle PQR has a right angle at R. The length of side PR is 9.8 cm, and the length of side QR is 6 cm. Sketch triangle PQR, and find ∠PQR, giving your answer correct to the nearest degree.

Answer 1

Answer on Question #61238 – Math – Trigonometry

Question

Triangle PQR has a right angle at R. The length of side PR is 9.8 cm, and the length of side QR is 6 cm. Sketch triangle PQR, and find ∠PQR, giving your answer correct to the nearest degree.

Solution

Given:

$$\angle PRQ = 90{}^\circ, |PR| = 9.8 \text{ cm}, |QR| = 6 \text{ cm}$$

Find ∠PQR

$$PQ = \sqrt{|PR|^2 + |QR|^2} = \sqrt{9.8^2 + 6^2} = \sqrt{132.04} \approx 11.49 \text{ (cm)},$$ $$\sin \angle PQR = |PR| / |PQ| = 9.8 / \sqrt{132.04} \approx 0.853,$$ $$PQR = \sin^{(-1)} 0.853 \approx 58.52{}^\circ \approx 59{}^\circ.$$

Answer: 59°

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