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Construct diagram, using all the data given in question. You will end up with 2 similar triangles. You will notice that length of ladder is the sum of hypotenuse of two small triangles.
Now find the length of hypotenuse of each small triangle in terms of angle (theta).
h1=3/sin(theta); h2=5/cos(theta)
length of ladder=h1+h2=3/sin(theta)+5/cos(theta)
now differentiate this expression w.r.t. angle(theta)
simplify this expression and put it equal to zero
-3cos(theta)/sin2(theta)+5sin(theta)/cos2(theta)=0
simplify this and you will get theta=0.70067
put this in expression for length of ladder to get answer 11.194m
(I solved this question with different values of length. The strategy is correct; however, numerical answers might be wrong)
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