Calculus Maximizing and Integrals

I have a question, because I'm doing this project with my partner for my Calculus class, and we're unsure of how to start and exactly what to do.

Here's what it states:

1. A sign on top of a 50 foot tall building is 10 feet tall. The company president asked you to find the best view of the sign, with pedestrians standing currently about 50 feet and are trampling the company's lawn because the sidewalk is 60 feet away from the building. You expressed a concern, and stated that the best view of the sign should be from 60 feet (on the sidewalk), instead of in the street. The sign must be replaced, so you are to determine a new size for the sign, so that the viewers are safely on the sidewalk 60 feet away from the building. The angle between the lines of sight from the observer's eye to the top and bottom of the sign is a measure of the observer's view of the sign, and best view occurs when the angle is the biggest; the observer's eyes are 5 feet from the ground (observer is 5' 3" tall). Determine the ideal viewing distance from the building when the sign is 10ft, the ideal distance is 49.7 ft. Determine the new sign height when the observer is 60 feet away.

Also, the company is considering putting a bench 35 feet away from the base of the building, so they should also know how tall the sign should be for the best view of the new sign at this distance too.

Any help is greatly appreciated. Thank you.

(Nerd)