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=7
𝑎
=
7
, b=24
𝑏
=
24
, and c=25
𝑐
=
25
.(1 point)
Responses

73.6 degrees
73.6 degrees

25.1 degrees
25.1 degrees

16.3 degrees
16.3 degrees

89.9 degrees

Answer 1

Use the Law of Cosines:

cos A = (b^2 + c^2 − a^2) / (2bc) = (24^2 + 25^2 − 7^2) / (2·24·25)
= (576 + 625 − 49) / 1200 = 1152 / 1200 = 0.96

A = arccos(0.96) ≈ 16.3 degrees.

Answer: 16.3 degrees.