It's that time of year again, your gutters need cleaning. You keep telling yourself you're going to install the screens this year but haven't yet. You forget which ladder your usually use, but you know your gutters are $16\text{'}$ off the ground and you want the ladder to be leaning at an angle $75$ from the ground for safety.

a$.$ Draw and label a diagram of the ladder in contact with the house and the ground.

b$.$ What is the minimum length of the ladder?

c$.$ What is the distance you need to keep clear around the house to safely move the ladder to clean all the gutters?