tricky question!!

[smilyfacebkwrm]

Two buildings are d units apart. A ladder 20 units long has its foot resting against building 1 and its top against the side of building 2. A second ladder 15 units long has its foot against building 2 and its top against the side of building 1. The ladders touch each other at a point c units above the ground.

a) show that (1/root 4-d^2) + (1/root 225-d^2) = 1/c

b) if d = 12, use part (a) to find c

c) if c=8, find d. since it is difficult to solve for d directly, you can use your calculator to approxmiate d to the nearest hundreth by finding the value of d for which the expressiong (1/root 4-d^2) + (1/root 225-d^2) - 1/8 changes sign

I can't get a and so I don't understand b or c either. I think with a I'd be able to do b, but not c... I can't get anywhere and I have no clue where to start with this.

 

[stapel]

A good place to start would probably be drawing a picture. Label all the given values (whether numerical or literal). Then name the other things, such as the heights of the tops of the ladders, and the bases of the triangles formed by the ground, the ladders, and the height-line with length "c".

Then use the Pythagorean Theorem and similar triangles, and see what you can come up with.

Note: I have a feeling that you're supposed to show, in (a), that 1/sqrt[400 - d²] + 1/sqrt[225 - d²] is what is equal to 1/c. You might want to proof-read that.

Eliz.

 

[Unco]

Two buildings are d units apart. A ladder 20 units long has its foot resting against building 1 and its top against the side of building 2. A second ladder 15 units long has its foot against building 2 and its top against the side of building 1. The ladders touch each other at a point c units above the ground.

a) show that (1/root 4-d^2) + (1/root 225-d^2) = 1/c

You can put them on some x-y axes.

              /|\ y
               |
sqrt(400-d^2)  +              /
               |            /
               |          /  
sqrt(225-d^2)  +        /
               |  *   /
               |     *
               |  /     *  
               |/          *
               +--------------+---------->
              0               d           x

Find the equations of the two lines.

Set their y-ordinates equal.

I'll let you figure out the rest.