Question

For ΔABC
Δ
𝐴
𝐵
𝐶
, find the measure of ∠C
∠
𝐶
to the nearest degree when side a=46
𝑎
=
46
m, side b=30
𝑏
=
30
m, and side c=20
𝑐
=
20
m. (1 point)
Responses

133 degrees
133 degrees

28 degrees
28 degrees

24 degrees
24 degrees

19 degrees
19 degrees

Answer 1

Use the Law of Cosines: cos C = (a^2 + b^2 − c^2) / (2ab).

cos C = (46^2 + 30^2 − 20^2) / (2·46·30) = 2616 / 2760 = 109/115 ≈ 0.947826.

C = arccos(0.947826) ≈ 18.6°, which rounds to 19°.

Answer: 19 degrees.