Question

Use the Law of Cosines, b2=a2+c2−2ac⋅cosB
, to find the value of angle B
in a right triangle, where a=9
, b=40
, and c=41
.(1 point)
Responses

84.55 degrees
84.55 degrees

77.32 degrees
77.32 degrees

78.01 degrees
78.01 degrees

90.01 degrees

Answer 1

Use the law of cosines:
cos B = (a^2 + c^2 − b^2) / (2ac)
= (81 + 1681 − 1600) / (2·9·41)
= 162 / 738 = 9/41.

So B = arccos(9/41) ≈ 77.32 degrees.

Answer: 77.32 degrees.