Question

Question #24864

Answer 1

`"ladder is 5 feet long"`

Explanation:

`"we can assume a right angle between the ground and"`
`"the building"`

`"using "color(blue)"Pythagoras' theorem"`

`("ladder")^2=3^2+4^2`

`color(white)(xxxxxx)=9+16=25`

`color(blue)"take the square root of both sides"`

`rArr"ladder " =sqrt25=5" feet"`

`"the result is a well known "color(blue)"Pythagorean triple"`

`"that is a " 3,4,5" triangle"`

`"others include"`

`5,12,13" and " 7,24,25`

`"these are worth knowing as they occur frequently"`

`"Pythagorean triples can be formed using"`

`n,(n^2-1)/2,(n^2+1)/2" for " n>=3`

`"for " n=9to9,40,41`