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: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 ftLadder distance from building ([tex]b_1[/tex]) = 7 ftThe top of ladder slip down to 4 ftLet p be the height of building.Now, using Pythagoras  formula to solve it[tex]p^{2} = h^{2} - b^{2}[/tex]Next putting the value in the formula[tex]p^{2} = 25^{2} - 7^{2} = 625 - 49[/tex]⇒ [tex]p= \sqrt{576} = 24[/tex]∴ Height of building (p) = [tex]24 \ ft[/tex]As ladder slip down to 4 ft∴ Now, the height from top of ladder to bottom of building = [tex]p-4 = 24 - 4= 20\ ft[/tex]Let [tex]b_2[/tex] be the base of ladder from building Again using Pythagoras  formula,[tex]b^{2} = 25^{2} - 20^{2} = 625 - 400[/tex]∴ [tex]b= \sqrt{225} = 15 ft [/tex][tex]b_2 = 15\ ft[/tex]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 = [tex]b_2- b_1[/tex]∴ Bottom of ladder slip = [tex]15 - 7= 8 \ ft[/tex]