SOLUTION: A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground. It is prevented from slipping by a tight rope PQ of lengt

Algebra ->  Trigonometry-basics -> SOLUTION: A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground. It is prevented from slipping by a tight rope PQ of lengt      Log On


   

Question 1132211: A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground. It is prevented from slipping by a tight rope PQ of length 1.6meters, fixed at P to the foot of the wall and at Q to the ladder, PQ being at the right angles to AB. Calculate in centimetres, the height AP of the ladder above P and length of the ladder..
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The picture is something like this....



Given QP = 1.6, there are many paths to finding the height AP and the length of the ladder AB; I will outline one of them. It is probably not the most efficient; it is simply the path I saw first.

I hope that you will get solution(s) from other tutor(s) using different paths to the answers.

I leave the actual calculations to you. Note that the given length of PQ is in meters; the answers are to be in centimeters.

(1) Find QB using right triangle PQB: tan%2871%29+=+PQ%2FQB+=++1.6%2FQB

(2) Find QA using similar triangles PQB and AQP: QA%2FPQ+=+PQ%2FQB --> QA%2F1.6+=+1.6%2FQB

(3) Find AP using right triangle APB: sin%2871%29+=+AP%2FAB+=+AP%2F%28QA%2BQB%29

As a check for the answers you get, my answers (in meters, to 1 decimal place) are AP = 4.9 and AB = 5.2.