Question

A 25-foot25−foot ladder is placed against a building. The bottom of the ladder is 77 feet from the building. If the top of the ladder slips down 44 feet, how many feet will the bottom slip?

Answer 1

Answer:

The bottom of ladder slip to 8 feet.

Step-by-step explanation:

Here is the given length or distance in question after avoiding typo error,

Length of ladder (h) = 25 ft

Ladder distance from building ($b_1$) = 7 ft

The top of ladder slip down to 4 ft

Let p be the height of building.

Now, using Pythagoras  formula to solve it

$p^{2} = h^{2} - b^{2}$

Next putting the value in the formula

$p^{2} = 25^{2} - 7^{2} = 625 - 49$

⇒ $p= \sqrt{576} = 24$

∴ Height of building (p) = $24 \ ft$

As ladder slip down to 4 ft

∴ Now, the height from top of ladder to bottom of building = $p-4 = 24 - 4= 20\ ft$

Let $b_2$ be the base of ladder from building

Again using Pythagoras  formula,

$b^{2} = 25^{2} - 20^{2} = 625 - 400$

∴ $b= \sqrt{225} = 15 ft$

$b_2 = 15\ ft$

Now, we have the distance of base of ladder from building after slip is 15 ft.

Next step is to find length of bottom of ladder further slip.

⇒ Bottom of ladder slip = $b_2- b_1$

∴ Bottom of ladder slip = $15 - 7= 8 \ ft$