Right cones and horizontal width

[KrabLord]

In the below problem, I cannot come to the conclusion that the book does. I cannot understand their reasoning for the solution, either.


Here’s their solution:


How does one reach the correct solution? I’m particularly puzzled by their measurements of the angles in the first part of the solution...

 

[Dr.Peterson]

See if this picture, with the given angles in green and the calculated ones in red, helps you see past the typos in the solution! (I think they intended to label the points on the picture as I have.)

You could also calculate DOA and DOB directly, rather than calculate the angles they show in the image.

I think their artist and writer weren't communicating well.