# Thread: Help required for Problem Sum on Applications of Trigonometry

1. ## Help required for Problem Sum on Applications of Trigonometry

Heres goes the question:
A ladder AB,of length 13m, rests against a vertical wallwith its foot on a horizontal floor at a distance of 5m from the wall. When the top of the ladder slips down a distance of x metres on the wall, the foot of the ladder moves out by x metres. Find the value of x.

Swift replies will be appreciated. Thanks in advance.

2. $\displaystyle (12-x)^2+(5+x)^2=13^2$
$\displaystyle 144-24x+x^2+25+10x+x^2=169$
$\displaystyle 2x^2-14x+169=169$
$\displaystyle x^2-7x=0$
$\displaystyle x = 0$ OR $\displaystyle (x-7) = 0$
$\displaystyle x = 0$ OR $\displaystyle x = 7$

Do you understand what I did?

$\displaystyle w^2 +5^2 = 13^2 \implies w=12$