Question 829545
For the ladder problem, the ladder is the hypotenuse.
Let h = height to the top of the ladder.
So h^2 + 3^2 = 12^2 , based on {{{a^2 + b^2 = c^2}}}
h^2 + 9 = 144
add -9 to each side.
h^2 = 135
take the square root of each side.
{{{h = sqrt(135)}}}
h = 11.62
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For the lawn that is 4 by 5, the diagonal is the hypotenuse.
(c=length of diagonal)^2 = 4^2 + 5^2
c^2 = 16 + 25
c^2 = 41
c = {{{sqrt(41)}}}
c = 6.403
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