Question

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

24 degrees
24 degrees

19 degrees
19 degrees

28 degrees
28 degrees

133 degrees

Answer 1

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

cos C = (a^2 + b^2 − c^2) / (2ab) = (46^2 + 30^2 − 20^2) / (2·46·30)
= 2616 / 2760 ≈ 0.947826.

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