Math  /  Trigonometry

QuestionQuestion 7, 6.1.1 HW Score: 44.449 Points: 0.330
Solve the triangle. B=74B=74^{\circ} (Do not round until the final answer. Then round to the nearest degree as needed.) b\mathrm{b} \approx \square (Do not round until the final answer. Then round to the nearest tenth as needed.) cc \approx \square (Do not round until the final answer. Then round to the nearest tenth as needed.)

Studdy Solution
Use the Law of Sines to find side c c :
asinA=csinC \frac{a}{\sin A} = \frac{c}{\sin C} 9sin32=csin74 \frac{9}{\sin 32^\circ} = \frac{c}{\sin 74^\circ}
Since C=B=74 C = B = 74^\circ , the calculation is similar to side b b :
c=9sin74sin32 c = \frac{9 \cdot \sin 74^\circ}{\sin 32^\circ}
Calculate c c (do not round until the final answer):
c90.96130.5299 c \approx \frac{9 \cdot 0.9613}{0.5299} c8.65170.5299 c \approx \frac{8.6517}{0.5299} c16.3 c \approx 16.3
The approximate lengths of the sides are: b16.3 b \approx 16.3 c16.3 c \approx 16.3

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