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Answered

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°

Verified Answer :

Edufirst

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 °
 

The correct answers are

Measure A - 58.15°

Measure C - 84.85 °

:)

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