Question

Solve the triangle A=46°,a=33,b=26.

a. Cannot be solved.
b. OB=34.5°,C=99.5°,c=45.2.
c..OB=34.5°,C=99.5°,c=27.1.
d. 2OB=34.5°,C=119.5°,C=36.2.

Answer 1

To solve the given triangle, we can use the Law of Sines and the Law of Cosines. By applying these formulas, we can determine the missing angles and side lengths.

Step-by-step explanation:

To solve the triangle, we need to determine the missing angle and side length. From the given information, we have A = 46°, a = 33, and b = 26. Using the Law of Sines, we can find the missing angle B: sin(B) = (b * sin(A)) / a. Plugging in the values, sin(B) = (26 * sin(46°)) / 33. Solving for B, we find that B ≈ 48.7°.

Next, we can find the missing side length c using the Law of Cosines: c² = a² + b² - 2ab * cos(C), where C is the missing angle. Plugging in the values, we have c² = 33² + 26² - 2 * 33 * 26 * cos(48.7°). Solving for c, we find that c ≈ 45.2.

Therefore, the correct option is (b) OB = 34.5°, C = 99.5°, c = 45.2.