Answer:
=A=
Find m∠C
- m∠C = 180° - (51° + 71°) = 58°
Find the missing sides using the law of sines:
- 9.8 / sin 71° = AB / sin 58° = AC / sin 51°
- AB = 9.8 sin 58° / sin 71° = 8.8 cm
- AC = 9.8 sin 51° / sin 71° = 8.1 cm
=B=
Find m∠L
- m∠L = 180° - (42° + 84°) = 54°
Find the missing sides using the law of sines:
- 50 / sin 84° = KL / sin 42° = JK / sin 54°
- KL = 50 sin 42 °/ sin 84° = 33.6 cm
- JK = 50 sin 54° / sin 84° = 40.7 cm
=C=
Find m∠R using the law of sines:
- 17.5 / sin 98° = 15 / sin ∠R
- sin ∠R = 15 sin 98° / 17.5
- sin ∠R = 0.85
- m∠R = arcsin (0.85) = 58.2°
Find the missing angle:
- m∠S = 180° - (98° + 58.2°) = 23.8°
Find the length of QR, use the law of sines:
- 17.5 / sin 98° = QR / sin 23.8°
- QR = 17.5 sin 23.8° /sin 98° = 7.1 m
