This is a popular problem but I have not seem to find the solution to it and I am in desperate need of help.

Two Poles Problem..
Two poles are 30 ft and 20 ft tall and are perpendicular to level ground. The two poles are 40 ft apart along the ground. If wires are attached to the top of each pole and are stretched taut to the bottom of the other pole, then find the height abouve the ground of intersection point of the two wire.

I know the height is 12.. but I need to show algebraically how I arrived there! Pleasssssssssee help.

Hello Brook:

Find the equations of the two intersecting lines, set equal and solve for x. y will follow.

Draw a picture. It always helps.

You have 4 sets of coordinates: (0,0), (40,0), (0,20), (40,30)

Use (0,0) and (40,30) to find the equation of that line.

Then use (0,20) and (40,0) to find the equation of the line.

Once you have the equations, set equal and solve for x. Then all you have to do is sub

that x value into one of your line equations to find y. Yes, it is 12.

I will do one line equation and you do the other. Okey-doke?

Slope is rise over run. m=\frac{y-y_{1}}{x-x_{1}}

So, we have: m=\frac{30-0}{40-0}=\frac{3}{4}

Now, use one of the given coordinates in y=mx+b. We just found m.

30=\frac{3}{4}(40)+b. Solve for b. b is where is crosses the y-axis. In this case it crosses at the origin, so b=0.

The equation of the line is y=\frac{3}{4}x

Now, finish? Find the equation of the other line the same way.

Another way:

From geometry 20/40 = x/z or 1/2 = x/z; 30/40 = x/y or 3/4 = x/y

Since y + z = 40, use the above to substitute for y and z in terms of x and you should come up with x = 12.

Hope this helps