In ΔABC, BC = 12.35, AC = 8.75 centimeters, and m∠B = 37°. What are

m∠A and m∠C to two decimal places?

m∠A ≈ 25.24°, m∠C ≈ 117.76°

m∠A ≈ 58.15°, m∠C ≈ 84.85°

m∠A ≈ 25.24°, m∠C ≈ 64.76°

m∠A ≈ 58.15°, m∠C ≈ 31.85°

Use the sine rule.

For any triangle: sin (a) / A = sin (b) / B = sin (c) / C

Where A is the side opposed to angle a, B is the side opposed to angle b, and C is the side opposed to angle c.

Here, sin (B) / AC = sin (A) / BC = sin (C) / AB

BC = 12.35, AC = 8.75 centimeters, and m∠B = 37°

sin (37) / 8.75 = sin (A) / 12.35 = > sin (A) = 12.35 * sin (37) / 8.75

sin (A) = 0.845 = A = arctan (0.845) = 58.15°

And A + B + C = 180° = > C = 180 - A - B = 180 - 58.15 - 37 = 84.85

Answer:

measure of angle A = 58.15°

measure of angle C = 84.85 °