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 trying to find angle A, so we'll use the formula a/sinA = b/sinC:

   6/sinA = 9/sin32

3. Solve for sinA:

   sinA = 6*sin32/9

4. Use a calculator to find the value of sinA:

   sinA ≈ 0.3499

5. To find angle A, take the inverse sine (also known as arcsin or sin^-1) of 0.3499:

   A = sin^-1(0.3499)

6. Use a calculator to find the value of A:

   A ≈ 20.53 degrees

So, the measure of angle A is approximately 20.53 degrees.