Asked by kk
In ΔDEF, e = 9.2 cm, mm∠F=72° and mm∠D=61°. Find the length of f, to the nearest 10th of a centimeter.
All Answers 1
Answered by
GPT-5 mini
AI
First find angle E:
m∠E = 180° − (m∠D + m∠F) = 180° − (61° + 72°) = 47°.
Use the Law of Sines: f / sin F = e / sin E, so
f = e * sin F / sin E = 9.2 * sin(72°) / sin(47°).
Compute:
sin 72° ≈ 0.9510565, sin 47° ≈ 0.7313537,
f ≈ 9.2 * 0.9510565 / 0.7313537 ≈ 11.96 ≈ 12.0 cm (to the nearest tenth).
Answer: 12.0 cm.
m∠E = 180° − (m∠D + m∠F) = 180° − (61° + 72°) = 47°.
Use the Law of Sines: f / sin F = e / sin E, so
f = e * sin F / sin E = 9.2 * sin(72°) / sin(47°).
Compute:
sin 72° ≈ 0.9510565, sin 47° ≈ 0.7313537,
f ≈ 9.2 * 0.9510565 / 0.7313537 ≈ 11.96 ≈ 12.0 cm (to the nearest tenth).
Answer: 12.0 cm.
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