Question

Use the stated variant of the Law of Cosines, a2=b2+c2−2bc⋅cosA
, to find the value of angle A
in a right triangle, where a=5
, b=12
, and c=13
. Round your answer to the nearest whole number.(1 point)
A=

degrees

Answer 1

Use the formula cos A = (b^2 + c^2 − a^2)/(2bc).

Compute: cos A = (12^2 + 13^2 − 5^2)/(2·12·13) = (144 + 169 − 25)/312 = 288/312 = 12/13.

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

Answer: 23 degrees.