A 30 ft. ladder reaches a height of 24 ft. when it is placed against a building and a 25 ft. ladder reaches 20 ft. The base of which ladder is further from the base of the building and by how many feet?

Question

A 30 ft. ladder reaches a height of 24 ft. when it is placed  against a building and a 25 ft. ladder reaches 20 ft.  The base of which ladder is further from the base of the building and by how many feet?

campbell_st · Answer

well you could assume they form right angled triangles... and use pythagoras

the ladders are the hypotenuses... 

and you would be finding a shorter side in both triangles.

anonymous · Answer

thats what we did in class but im really confused

campbell_st · Answer

ok... 

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use the triangles I've drawn

anonymous · Answer

so the actual height of the ladder doesn't matter

anonymous · Answer

@campbell_st

campbell_st · Answer

well the height of the ladder is the hypotenuse of the right triangles  so using pythagoras you have 

$$x^2 = 30^2 - 25^2$$

and 

$$y^2 = 24^2 - 20^2$$

campbell_st · Answer

when you get the answers, take the square root of both to find out how far the base of each ladder is from the wall..

anonymous · Answer

ok i got it now

anonymous · Answer

thx