Question

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

14.5 degrees
14.5 degrees

17.3 degrees
17.3 degrees

13.1 degrees
13.1 degrees

12.7 degrees

Answer 1

Use the Law of Cosines:
cos A = (b^2 + c^2 − a^2) / (2bc)
= (40^2 + 41^2 − 9^2) / (2·40·41)
= (1600 + 1681 − 81) / 3280
= 3200 / 3280 = 40/41.

So A = arccos(40/41) ≈ 12.7 degrees.

(Answer: 12.7 degrees.)