Question

Solve each triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree.

A = 50°, B = 30°,c = 9

Answer 1

To solve the triangle with angles A = 50°, B = 30°, and side c = 9, we can use the Law of Sines and Law of Cosines. The side lengths are approximately a = 6.3, b = 7.4, and the missing angle is 100°.

Step-by-step explanation:

To solve the triangle with angles A = 50°, B = 30°, and side c = 9, we can use the Law of Sines and Law of Cosines.

1. First, we can use the Law of Sines to find the ratios of the side lengths to the sine of their opposite angles. We have sin(A)/a = sin(B)/b = sin(C)/c. Plugging in the values, we get sin(50°)/a = sin(30°)/9. Solving for a, we find a ≈ 6.3.
2. Next, we can use the Law of Cosines to find the remaining side length. The formula is c^2 = a^2 + b^2 - 2ab*cos(C). Plugging in the known values, we get 9^2 = 6.3^2 + b^2 - 2*6.3*b*cos(50°). Solving for b, we find b ≈ 7.4.
3. Finally, to find the missing angle, we can use the fact that the sum of the angles in a triangle is 180°. The missing angle can be found by subtracting the given angles from 180°: 180° - 50° - 30° = 100°.

Therefore, the side lengths of the triangle are approximately a = 6.3, b = 7.4, and the missing angle is 100°.