Solve for the remaining angles and side of the triangle described below. Round to the nearest thousandth:C=70°𝐶=70°, a=5𝑎=5, b=3

To solve for the remaining angles and side of the triangle, we can use the Law of Sines and the fact that the sum of the angles in a triangle is 180°.

Step 1: Solve for angle A using the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. So, we have:

sin(A)/a = sin(C)/b

Substituting the given values, we get:

sin(A)/5 = sin(70°)/3

Solving for sin(A), we get:

sin(A) = 5 * sin(70°) / 3

Calculating the above expression, we get:

sin(A) ≈ 1.128

However, the value of sin(A) cannot be greater than 1, so there seems to be a mistake. The problem lies in the fact that the given sides a and b with the given angle C do not satisfy the sine rule. The side b is too short to form a triangle with the given angle C and side a. Therefore, the triangle as described cannot exist.