1A13.5 cm 8.3 cmCB32°The diagram shows triangle ABC, with .AC 13 5cm= , .BC 8 3cm= and angle ABC 32°= .Find angle CAB

To find angle CAB in triangle ABC, 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 how you can apply it:

1. First, let's denote angle CAB as α. We know that BC = 8.3 cm, AC = 13.5 cm, and angle ABC = 32°.

2. According to the Law of Sines, we have sin(ABC)/BC = sin(CAB)/AC.

3. Substituting the known values, we get sin(32°)/8.3 = sin(α)/13.5.

4. Solving for sin(α), we get sin(α) = (sin(32°) * 13.5) / 8.3.

5. To find α, we take the inverse sine (sin^-1) of the result from step 4.

6. Therefore, α = sin^-1[(sin(32°) * 13.5) / 8.3].

7. Use a calculator to compute this value. Make sure your calculator is set to degrees, not radians.

This will give you the measure of angle CAB in degrees.