Final answer:
To find the other angles of a triangle given the lengths of its sides, we can use the Law of Cosines. Using the Law of Cosines, we can calculate the angles A and B of the triangle with the given side lengths. Angle A is approximately 23.6° and angle B is approximately 53.1°.
Step-by-step explanation:
To find the other angles of a triangle given the lengths of its sides, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2ab * cos(C).
In this specific case, we are given a = 23in, b = 37in, and c = 41in. Let's denote angle A opposite side a, angle B opposite side b, and angle C opposite side c. We can use the Law of Cosines to find angle A and angle B.
Using the Law of Cosines, we can calculate:
- cos(A) = (b^2 + c^2 - a^2) / (2bc)
- cos(B) = (a^2 + c^2 - b^2) / (2ac)
After calculating the values of cos(A) and cos(B), we can find their corresponding angles by taking the inverse cosine (arccos) of each value. Round the angles to the nearest degree to get the final answers.
Angle A is approximately 23.6° and angle B is approximately 53.1°.