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Easy/Hard, i dunno, but i cant do it

Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
Reply 1
Avatar for k@tie
k@tie
10
see attached
maths.gif7.3KB
Reply 2
Avatar for r_perry
r_perry
OP
i tried the similar triangles method, same as katie, and got a quatic, used the newton rahpson and then got the distance to be around 16.2
Reply 3
Avatar for k@tie
k@tie
10
r_perry
i tried the similar triangles method, same as katie, and got a quatic, used the newton rahpson and then got the distance to be around 16.2

:redface: you can't do that! Numerical methods suck - try again and get a proper answer :-P <lol I gave up btw :wink:>
[attached
hint
treat the bottom left as (O,O)
find the equations of the lines
use (C.,8) as the Intersection
now Pyhag


etc 1
Reply 5
Avatar for manps
manps
9.1cm through some weird method, cant even see how i got it now :confused:
Reply 6
Avatar for zxczxc
zxczxc
11
I might be wrong, very wrong, and oversimplifying it, but can't you just work out the angle between the trees and the ground using simple trigonometry, and then work out the distance between the foot of each tree and the crossover point, then add? In which case it would be 23.62.
Reply 7
Avatar for BCHL85
BCHL85
12
r_perry
i tried the similar triangles method, same as katie, and got a quatic, used the newton rahpson and then got the distance to be around 16.2

I got the same answer with you.
Use similar triange to end up with quartic equation, then somehow find the solution. I used iterative method to find it.
Reply 8
Avatar for animal555
animal555
r_perry
Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?


seems like there could be a number of solutions, but assuming the trees lie by either wall isn't the distance between the foot of each tree the distance between the walls?
Reply 9
Avatar for BCHL85
BCHL85
12
animal555
seems like there could be a number of solutions, but assuming the trees lie by either wall isn't the distance between the foot of each tree the distance between the walls?

I got the quartic equation ... but because the distance must be smaller than 20 ... so I think there's only 1 solution d = 16.2..

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