Dr. black is standing 13 feet from a street lamp. the lamp is making his shadow 9 feet long. he estimates that the angle of elevation from the tip of his shadow to the top of the street lamp is 50 degrees. to the nearest door, the street lamp is about

To clarify your question, the last part. Is it to the nearest foot or door? If you meant door then your answer is:

13 + 9 = 22 feet
the angle is 50 degrees
multiply 22 x tan(50) to find the height of the lamppost
22 x tan(50) = 26.21 so the lamppost is about 26 feet tall

Because one letter represents an endpoint and the other doesn't.

Step-by-step explanation:

Ray AB starts at endpoint A and goes through point B and then on, indefinitely.

Ray BA starts at endpoint B and goes through point A and then on, indefinitely.

They 'point' in opposite directions.