a ladder is 13 ft long leaning against the wall. the bottom is 5 ft from the wall. how much should the bottom be pulled away to move the ladder down two ft.

Question

a ladder 13 ft long leans against a wall. the bottom is 5 ft from the wall. How much would the lower end of the ladder have to be moved away from the wall so that the top end of the ladder would be pulled down 2ft.

Answer 1

First find the height of the ladder on the wall initially.

Use the Pythagorean Theorem to determine this.

 

a² + b² = c²                           where: a = 5 ft, b = height ft, c = 13 ft

 

5² + b² = 13² 

 

25 + b² = 169                         this implies that 169 - 25 = b²  therefore b = √169-√25 = √144 = 12 ft

 

 

Move the ladder down 2 ft gives a height of 12 ft- 2 ft = 10 ft. Now calculate the distance the ladder is from the bottom of the wall.

 

√13² - √10² = √69 = 8.3 ft.

 

So the ladder must be moved 8.3 ft - 5 ft = 3.3 ft away from the wall . Answer