Question

Solve the following triangle. B = 40°, C = 60°, b = 10 A = ____ ° (Simplify your answer.) a = ____ (Type an integer or decimal rounded to two decimal places as needed.) c = ____ (Type an integer or decimal rounded to two decimal places as needed.)

Answer 1

To solve the triangle, we calculate angle A as 80°. By using the law of sines, we find side a = 10.39 and side c = 12.99.

Step-by-step explanation:

To solve the following triangle, we need to use both the law of sines and the law of angles. As we know, the sum of the angles in a triangle is always 180°, so we can calculate angle A = 180° - (B + C) = 180° - (40° + 60°) = 80°.

Next, we can find the lengths of sides a and c using the law of sines:

For side a, we have sin(A)/a = sin(B)/b. Plugging in values, we have sin(80°)/a = sin(40°)/10. Solving for a, we find a = 10 * sin(80°) / sin(40°) = 10.39, which can be rounded to 10.39.

For side c, similarly, we have sin(C)/c = sin(B)/b. Plugging in values, we give sin(60°)/c = sin(40°)/10. Solving for c, we find c = 10 * sin(60°) / sin(40°) = 12.99, rounded to 12.99.

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