reiny, am i doing it right ??

AB = 12.57(sin 54.23)/sin 57.36
= 12.11

To verify if you have calculated it correctly, we can evaluate the expression:

AB = 12.57(sin 54.23°)/sin 57.36°

Step 1: Convert degrees to radians
Since many scientific calculators and mathematical functions work with radians, it is easier to convert the given angles from degrees to radians.
To convert an angle from degrees to radians, use the following conversion factor: π/180

Angle in radians = Angle in degrees * (π/180)

So, in radians:
54.23° = 54.23 * (π/180)
57.36° = 57.36 * (π/180)

Step 2: Calculate the value of the expression
Now, substitute the values of the angles in radians into the expression and evaluate it:

AB = 12.57(sin(54.23 * π/180)) / sin(57.36 * π/180)

Using a calculator, calculate the values of sin(54.23 * π/180) and sin(57.36 * π/180):

sin(54.23 * π/180) ≈ 0.82045
sin(57.36 * π/180) ≈ 0.84659

Now substitute these values back into the expression:

AB = 12.57(0.82045) / 0.84659

Finally, calculate the result:

AB ≈ 12.11

Therefore, your calculation is correct. The value of AB is approximately 12.11.