can you answer

Question

A ladder 10 ft long leans against a wall. The bottom of the ladder is 6ft from the wall. The bottom of the ladder is then pulled out 3 ft bottom of the ladder is then pulled out 3 ft farther. How much does the top end move down the wall?

Answer 1

Hi Bill,

 

So the ladder leaning against the wall forms a right triangle

 

the hypothenuse of the triangle is the ladder and is 10ft

 

one leg is 6ft and using the pythagorean theorem

 

10² = 6² + x²

 

100 - 36 = x²

 

64 = x²

 

x = 8

 

when we move the bottom of the ladder out 3 ft the leg now becomes 9ft

 

so

 

10² = 9² + x²

 

100 - 81 = x²

 

19 = x²

 

x = sqrt(19)

 

so the ladder was 8ft up on the wall and then it moved to sqrt(19)ft up on the wall

 

so the ladder moved down the wall 8-sqrt(19)

 

hope this helps