Final answer:
The other angles of the triangle are approximately 30.1°, 48.7°, and 101.2°.
Step-by-step explanation:
Given the side lengths of a triangle a = 23 in., b = 37 in., and c = 41 in., we can use the Law of Cosines to find the other angles of the triangle. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides times the cosine of the angle between them.
Using the Law of Cosines, we can find the angle A opposite side a:
A = arccos((b^2 + c^2 - a^2)/(2bc))
Similarly, we can find the angles B and C:
B = arccos((a^2 + c^2 - b^2)/(2ac))
C = arccos((a^2 + b^2 - c^2)/(2ab))
Plugging in the given side lengths, we can calculate the angles A, B, and C to the nearest degrees as follows:
A ≈ 30.1°
B ≈ 48.7°
C ≈ 101.2°