Final answer:
To solve the triangle using the Law of Sines, we can first sketch the triangle given the angles and side length. Then, we can use the Law of Sines equation and plug in the values to find the lengths of the other two sides of the triangle.
Step-by-step explanation:
To solve the triangle using the Law of Sines, let's first sketch the triangle. We are given that angle B is 29°, angle C is 51°, and side b is 44. Angle A can be found by subtracting angles B and C from 180°: A = 180° - 29° - 51° = 100°. Now, we can use the Law of Sines:
a/sin A = b/sin B = c/sin C
Plugging in the given values, we have:
a/sin(100°) = 44/sin(29°) = c/sin(51°)
Let's solve for side a and side c:
a = sin(100°) * (44/sin(29°)) ≈ 63.956
c = sin(51°) * (44/sin(29°)) ≈ 94.975
Therefore, the lengths of side a and side c are approximately 63.956 and 94.975, respectively.