I have two Right Triangle Word Problems that I can't figure out

Question

1. You're going to paint the trim along the ceiling in a fancy house. The trim is 16 feet off the ground. You want the top of your 18 foot ladder to reach 12-13 feet up the wall to make reaching the trim easier. What range of the angles will work to get you between 12 and 13 feet?
2. A security camera at a bank is set up to aim at the door and set images of the faces of incoming customers. The camera is mounted at a height of seven feet. The wall on which it is mounted is twenty feet from the door. Since this is a fixed camera, they are aiming to focus at a height of 67 inches (average customer height). What angle should the camera make with the wall?

Ive been trying to solve these for so long and I'm getting frustrated! Any explanation on how I need to go about solving these is appreciated. Thank You.

Answer 1

1) In a right triangle, if A is one of the non-right angles, H is the hypotenuse and O is the side opposite A, then sine of A = O/H. Since we know H is 18 and O is between 12 and 13, sine of A ranges between 2/3 and 13/18. From there, you can figure the range of A.

2) this is similar to the previous, except in this case we know the adjacent side and the opposite side. The opposite side is the distance from the wall to the focus point or 240 inches. The adjacent side is the distance below the mounting point height to the focus point height; 84-67 or 17 inches. The appropriate trig function in this case is tangent A = opposite/adjacent = 240/17. From there, you can figure the mounting angle.