Question

a 3ft tall boy casts a 4ft shawdow at the same time a tree casts a 72 foot shawdow using the pythagorean therem find the distance from the top of the tree to the tip of the shawdow

Answer 1

the Pythagorean Theorem is not what you need here.

The boy is 3/4 as tall as his shadow.
The tree is 3/4 as tall as its shadow.

so, what's 3/4 of 72?

You could use the theorem to find the distance from the boy's head to the tip of his shadow (d^2 = 3^2 + 4^2)
but that still wouldn't help you find the height of the tree. You'd still have to fall back on using similar triangles.

Answer 2

approximate to the nearest inch the lenght of a rectangle whose diagnol measures 25.0 inches and whose width is 18.0

Answer 3

Now you can use your theorem:

If the length is x, then

x^2 + 18^2 = 25^2
x^2 = 625 - 324
x^2 = 301
x = 17

Answer 4

a ladder 39 ft long leans against a building and reaches the ledge of a window if the foot of the ladder is 15 ft from the foot of the building how high is the window ledge above the ground tot the nearest foot.

Answer 5

come on. this is just like the one I just did for you. show me whatcha got. I'll let you know whether anything's amiss.