Question

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

90.01 degrees
90.01 degrees

84.55 degrees
84.55 degrees

78.01 degrees
78.01 degrees

77.32 degrees
77.32 degrees

Answer 1

Use the law of cosines: cos B = (a^2 + c^2 − b^2) / (2ac).

Compute: (81 + 1681 − 1600) / (2·9·41) = 162 / 738 = 9/41.

Thus B = arccos(9/41) ≈ 77.32 degrees.