2016-09-20 05:55:21
A painter wants to lean a 30-foot ladder against a wall. Safety guidelines recommend that the distance between the base of the ladder and the wall should be 1/4 of the length of the ladder. To the nearest degree, what acute angle should the ladder make with the ground? Enter only the number. (Hint: Sketch the problem first. )
2016-09-20 10:33:12

This is going to be a right triangle made with the floor the ladder and the wall so... (30)(.25)= 7.5 this means the ladder is 30 feet long and the distance between the floor and the wall is 7.5 feet. Then we can use the Pythagorean theorem to find the last side, a^2+b^2=c^2,  a^2+7.5^2=30^2. using basic algebra we can find that the distance of the last side (wall) is 29.0473751 about 29.05. Then using soh cah toa we can find the angles. To find the angle the ladder makes with the ground use tangent, tan(29.05/7.5). Your answer should be 67 degrees