If a 16' ladder is placed correctly on a level surface, how high up will the ladder reach? So i have just began learning about sin cos and tan, and i came across this problem and for some reason I'm having trouble figuring it out. *** When using a straight ladder, it is recommended that the base of the ladder by place approximately 1/4 length of the entire ladder away from the wall. a) If a ladder is placed correctly on a level surface, what is the angle formed between the ground and the ladder? b) If a 16' ladder is placed correctly on a level surface, how high up will the ladder reach? So i understand that cos = adjacent / hypotenuse And that the distance of the ladder is 4' away from the wall but I'm lost from there.

A. Here, you should use cosine as you stated. Set up an equation in the format you described: cos(theta) = 4/16. Then, you use something called arccos, which is just cos^(-1). This crosses out the cos on the left side, and you end up with theta = arccos(1/4). Plug this into your calculator to get your answer: 75.52248781.

B. Finding the how high the ladder goes is easy. You just use the Pythagorean Theorem. One leg is 4 feet and the hypotenuse is 16 feet, so the other leg needs to be 4*sqrt(15).