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I came across this problem on math stack exchange and tried to solve it myself: The position of a ladder leaning against a wall and touching a box under it.

What I did was set up 2 equations

$(x+1)^2+(y+1)^2=4^2$

$x^2+1^2=(4-(1+y)^2)^2$

Then by similar triangles:

$x/(x+1)=1/(1+y)$

I took $(x+1)^2+(y+1)^2=4^2$ then solved for 1+y to get $sqrt(-x^2-2x-15)$

I then plugged this back into the original and got

$x+1/x = 1/(-x^2-2x-15)$

However, my equation gives complex solutions. So where have I gone wrong? How can I get to the right solution using these 2 equations?

Ethan Chan
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1 Answers1

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The problem is in the step in which you solve the equation $(x+1)^2+(y+1)^2=4^2$. You should have obtained$$y+1=\pm\sqrt{15-x^2-2x}.$$

José Carlos Santos
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