"we can assume a right angle between the ground and"we can assume a right angle between the ground and
"the building"the building
"using "color(blue)"Pythagoras' theorem"using Pythagoras' theorem
("ladder")^2=3^2+4^2(ladder)2=32+42
color(white)(xxxxxx)=9+16=25×××=9+16=25
color(blue)"take the square root of both sides"take the square root of both sides
rArr"ladder " =sqrt25=5" feet"⇒ladder =√25=5 feet
"the result is a well known "color(blue)"Pythagorean triple"the result is a well known Pythagorean triple
"that is a " 3,4,5" triangle"that is a 3,4,5 triangle
"others include"others include
5,12,13" and " 7,24,255,12,13 and 7,24,25
"these are worth knowing as they occur frequently"these are worth knowing as they occur frequently
"Pythagorean triples can be formed using"Pythagorean triples can be formed using
n,(n^2-1)/2,(n^2+1)/2" for " n>=3n,n2−12,n2+12 for n≥3
"for " n=9to9,40,41for n=9→9,40,41
