Final answer:
The Law of Sines is used to solve triangles when you know the measures of two angles and one side or two sides and an included angle. In this case, use the sine ratio to find the missing angle in the given triangle.
Step-by-step explanation:
The Law of Sines is used to solve triangles when you know the measures of two angles and one side or two sides and an included angle. In this case, we want to solve the triangle with angle B equal to 35.4 degrees, side b equal to 29 units, and side c equal to 33 units. To solve for the missing angle, we can use the sine ratio:
sin A / side a = sin B / side b
Plug in the given values:
sin A / a = sin 35.4° / 29
Now, cross multiply and solve for sin A:
sin A = (a * sin 35.4°) / 29
Since sin A = sin (180° - A), we can find the two possible values for angle A. Use the inverse sine function (sin-1) on both sides:
A = sin-1((a * sin 35.4°) / 29)
Calculate both values for A and you will have two possible solutions for the triangle.