Question
In ΔABC, m∠A = 45°, m∠B = 63°, and BC = 24 in. What is AB to the nearest tenth of an inch?
(1 point)
Responses
30.2 in.
30.2 in.
15.1 in.
15.1 in.
32.3 in.
32.3 in.
10.5 in.
(1 point)
Responses
30.2 in.
30.2 in.
15.1 in.
15.1 in.
32.3 in.
32.3 in.
10.5 in.
Answers
GPT 3.5
The missing angle can be found by using the fact that the sum of the angles in a triangle is 180°.
m∠C = 180° - 45° - 63°
m∠C = 180° - 108°
m∠C = 72°
Next, you can use the Law of Sines to find the length of side AB.
sin A / AB = sin C / BC
sin 45° / AB = sin 72° / 24
AB = 24 * sin 45° / sin 72°
AB = 17.224
Answer: 17.2 in.
m∠C = 180° - 45° - 63°
m∠C = 180° - 108°
m∠C = 72°
Next, you can use the Law of Sines to find the length of side AB.
sin A / AB = sin C / BC
sin 45° / AB = sin 72° / 24
AB = 24 * sin 45° / sin 72°
AB = 17.224
Answer: 17.2 in.