In ΔABC, b = 2 inches, c = 4.1 inches and ∠A=145°. Find ∠B, to the nearest 10th of an degree.

To solve this problem, we will use the Law of Sines, which 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.

The formula is: a/sinA = b/sinB = c/sinC

We know the values of b, c, and ∠A, and we want to find ∠B.

First, we need to find the value of sinA. Since ∠A = 145°, we can use a calculator to find that sinA ≈ -0.8192.

Next, we substitute the known values into the formula:

2/sinB = 4.1/-0.8192

Solving for sinB, we get sinB = 2 * -0.8192 / 4.1 ≈ -0.4

Finally, we find the angle whose sine is -0.4. Using a calculator, we find that ∠B ≈ -23.6°.

However, in the context of a triangle, an angle cannot be negative. The negative result indicates that the angle is in the third or fourth quadrant (measured from the positive x-axis), but in a triangle, the angle should be in the first or second quadrant.

Therefore, we add 180° to the result to get the angle in the correct quadrant.

∠B = -23.6° + 180° = 156.4°

So, ∠B is approximately 156.4°.