Geometry Question: Anyone older than 14 should be able to do this (yes, I am challenging you)?

Question

Hi everybody, I wanted to see how well you guys and girls are able to do geometry, and how good you are, whether you are 11 or 51, let's see if you can solve this simple problem. The first one to answer correctly gets ten bonus points! (NOTE: You must show as much work as possible to get credit)

Okay folks, here's the problem:

In a field, there are two telephone poles, perpendicular to the ground. The first pole is 30 feet tall, and the second one is 20 feet tall. Each pole has a wire extended from the its own top to the other's base. Here's the tricky part. If the poles are fifty feet away, and the field is perfectly flat, at what point do the two wires cross?

Okay people, let's see if you can get it.

HINT: Use the pythagorean theorem (a^2+b^2=c^2), and then go from there.

IM SORRY GUYS! You are supposed to find the crossing point in reference to how HIGH it is off the ground! I'm so sorry, I hope you will adjust your answers accordingly.

Answer 1

Okay, here goes.

a^2+b^2=c^2, therefore sqrt(a^2+b^2)=c
sqrt(50^2+20^2)=c
sqrt(2500+400)=c
sqrt(2900)=c
c=53.8516 for 20 ft pole

sqrt(50^2+30^2)=c
sqrt(2500+900)=c
sqrt(3400)=c
c=58.3095 for 30 ft pole

x=58.3095-53.8516
x=4.4579

Crossing point is 4.4579 feet from 20 ft pole.

Hopefully I'm right!

Answer 2

30 feet from the 30 foot pole, 12 feet above the ground

Answer 3

Equation for first wire (30' pole to ground)
y1 = -(30/50)x + 30

For second wire:
y2 = (20/50)x +0

Intersection @ y1=y2
-(30/50)x + 30 = (20/50)x

x = 30 feet

Answer 4

I would have taken a different route to the solution. Work out a linear equation for each of the wires and then find the value of x for each which has the same value of y (i.e. simultaneous equation)

More than one way to skin a cat. :-)