Maths problem!!!?

[lost soul]

A firefigher has to get into a building through a window by leaning his 5m ladder against a wall.

1) Draw a distance to show this situation using xm for the distance up the wall.

2) Write down Pythagros' Theorem using the terms from your diagram.

3) if th eladder is against the wall with the foot of the ladder 3m from the wall, at what height does the ladder touch the wall?

4)The firefighter is in such a hurry that the end of the ladder slips a certain distance (p) meters away from the wall, touching the wall (n) meters lower. use your pythagorean equation with the changed terms. Show that this equation can be written as p^2+n^2=8n-6p.

5) using the same methods as in 4, find an equation if the ladder is pushed in (p) meteres from the original 3 m mark from the wall.

6) if the height up a wall is a - b and the distance of the foot of the ladder is a + b, show that the length of theladder can be written as (square root) 2(a^2+b^2).
7) compare your answers to 4 and 5 and explain.

8) writing the length of the ladder as 5, the height reached up the wall is twice a - b and the distance to the wall is a third of a + b, show that if a = 3, then 37b^2 - 210b = 108.


tahnks heaps!!!

do as many you could!!