Answer:
√(25+12√2) ≈ 6.48
Explanation:
You want the length of the longest side, labeled x, in the obtuse triangle with sides of lengths 3 and 4 and angle 135° between.
Law of Cosines
The law of cosines tells you ...
c² = a² +b² -2ab·cos(C)
Using this here, we have a=4, b=3, C=135°:
x² = 4² +3² -2·4·3·cos(135°)
x² = 25 -24(-√2/2) = 25 +12√2
x = √(25 +12√2) ≈ 6.48