Question

Use the stated variant of 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=5
𝑎
=
5
, b=12
𝑏
=
12
, and c=13
𝑐
=
13
. Round your answer to the nearest whole number.(1 point)
A=
𝐴
=
degrees

Answer 1

Use the law of cosines:
cos A = (b^2 + c^2 − a^2) / (2bc) = (144 + 169 − 25) / (2·12·13) = 288 / 312 = 12/13.

So A = arccos(12/13) ≈ 22.62°, which rounds to 23°.

A = 23 degrees.