To calculate the unknown sides and angles in triangle ABC, use the Law of Sines and the Law of Cosines. Angle A is approximately 53.1°, angle B is approximately 68.8°, angle C is approximately 58.1°, and side b is approximately 12.5m.
To calculate the unknown sides and angles in triangle ABC, we can use the Law of Sines and the Law of Cosines.
First, let's find angle A using the Law of Sines:
sin(A) = a / c
sin(A) = 10 / 8.5
A ≈ 53.1°
Next, we can find angle B:
angle B = 180° - angle A - angle C
angle B ≈ 180° - 53.1° - 58.1°
angle B ≈ 68.8°
Now, we can find angle C:
angle C = 180° - angle A - angle B
angle C ≈ 180° - 53.1° - 68.8°
angle C ≈ 58.1°
Finally, we can find side b using the Law of Cosines:
b² = a² + c² - 2ac * cos(B)
b² = 10² + 8.5² - 2 * 10 * 8.5 * cos(68.8°)
b ≈ 12.5m