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

measure of angle A = 58.15°
measure of angle C = 84.85 °