The proper angle for a ladder is about 75 ∘ 75∘ from the ground. suppose you have a 14 foot ladder. how far from the house should you place the base of the ladder?

We just use the sinus rule to calculate this

a / sin alpha = b / sin beta

Alpha is the 90 degree angle from the wall to the floor

beta is the angle from the top of the ladder to the wall,

wich is 90 degrees - 75 degrees (triangle has 180 degrees angles, one is 90 degrees), so beta = 15 degrees

14 foot / sin 90 = b / sin 15

sin 90 = 1

we move the sin15 over to the other side

14 foot x sin 15 = b

b = 3.62 foot