In triangle ABC ,AP is perpendicular to BC ,BC = 112 cm , cot B = 4/3 , cot C =12/5 . find the length of AP
Answers
Answered by
3
Given, ABC is triangle, where BC = 112 cm
Again, AP is perpendicular to BC
Let PC = x
then BP = 112 - x
Now, triangle APC,
tan C = AP/PC
=> 1/cot C = AP/x
=> 1/(12/5) = AP/x
=> 5/12 = AP/x
=> AP = 5x/12 ...........1
Again, in triangle APB,
tan B = AP/PB
=> 1/cot B = AP/(112 - x)
=> 1/(4/3) = AP/(112 - x)
=> 3/4 = AP/(112 - x)
=> AP = 3(112 - x)/4 ...........2
From equation1 and 2, we get
=> 5x/12 = 3(112 - x)/4
=> 5x = {3 * 12(112 - x)}/4
=> 5x = 3 * 3(112 - x)
=> 5x = 9(112 - x)
=> 5x = 9 * 112 - 9x
=> 5x + 9x = 9 * 112
=> 14x = 9 * 112
=> x = (9 * 112)/14
=> x = 9 * 8
=> x = 72
From, equation 1, we get
AP = (5 * 72)/12
=> AP = 5 * 6
=> AP = 30 cm
So, the length of AP is 30 cm
Similar questions