From the oblique triangle in which a = 6 cm, b= 9 cm and C = 32 degrees, solve for the angle A.

To solve for angle A in the oblique triangle, we can use 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.

Here's the step-by-step solution:

1. Write down the Law of Sines formula: a/sinA = b/sinB = c/sinC

2. Substitute the given values into the formula. We know a = 6 cm, b = 9 cm, and C = 32 degrees. We're solving for A, so we'll use the formula a/sinA = b/sinC:

   6/sinA = 9/sin32

3. Solve for sinA:

   sinA = 6*sin32/9

4. Calculate the value of sinA using a calculator. Make sure your calculator is set to degrees, not radians.

5. Once you have the value of sinA, find the angle A by taking the inverse sine (also known as arcsin or sin^-1) of the value you calculated. This will give you the measure of angle A in degrees.

Remember, the Law of Sines can give an ambiguous case (two possible solutions for a triangle), but in this case, since the given angle C is acute and side a is shorter than side b, there is only one possible solution.