Math  /  Trigonometry

Question1. Determine each unknown side length to the nearest tenth. a) b)

Studdy Solution
For triangle PQR, use the Law of Cosines to find side r r :
The Law of Cosines states: r2=p2+q22pqcos(R) r^2 = p^2 + q^2 - 2pq \cdot \cos(R)
Substitute the known values: r2=12.02+9.022×12.0×9.0×cos(125) r^2 = 12.0^2 + 9.0^2 - 2 \times 12.0 \times 9.0 \times \cos(125^\circ)
Calculate: r2=144+81216×cos(125) r^2 = 144 + 81 - 216 \times \cos(125^\circ)
r2=225216×cos(125) r^2 = 225 - 216 \times \cos(125^\circ)
Calculate cos(125) \cos(125^\circ) using a calculator, then compute r2 r^2 .
Find r r by taking the square root and round to the nearest tenth.
STEP_2.1: Calculate cos(125) \cos(125^\circ) and complete the computation for r r .
cos(125)0.5736 \cos(125^\circ) \approx -0.5736
r2=225216×(0.5736) r^2 = 225 - 216 \times (-0.5736)
r2=225+123.4176 r^2 = 225 + 123.4176
r2=348.4176 r^2 = 348.4176
r=348.4176 r = \sqrt{348.4176}
r18.7 r \approx 18.7
The unknown side lengths are:
a) c6.2 c \approx 6.2
b) r18.7 r \approx 18.7

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