Question

find the approximate length of the leg of a right triangle with one leg length 8 and hypotenuse length 19

Answer 1

Pythagorean :

hypotenuse^2= base^2+height ^2
19^2=8^2+height ^2
height^2=(19-8)(19+8)
height ^2=11.27
height ~17,74

Answer 2

So, teh exact value is sqrt( 19^2 - 8^2 ) = sqrt( 361-64) = sqrt(297).

There's people who can calculate this mentally, but I can't. Approximate by known squares: 15^2 = 225, 16^2 = 256, 17^2= 289, 18^2=324,

So, 18.