Given Right Triangle has side b=5, B=15 degrees. I calculated: sin 15 = 5/H which results in H = 7.69. But H is actually 19.73 What is wrong with my equation and/or calculation.
Yes, sa-ri-ga-ma is right. In these types of situations where it says that the angle is 15 degrees, then you must out your calculator in degrees mode.
The answer you got, H = 7.69, was when you used sin(angle) in radians.
If you don't know how to get degrees on your calculator, then you can convert degrees into radians by:
$\displaystyle angle * \pi{ } / 180$
and that will convert your angle from degrees to radians.