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Two sides of a triangle have lengths a and b and the angle between them is angle theta. What value of angle theta will maximize the triangle's area? Use the formula A=1/2absintheta.
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1 Answer

Given, the area of a triangle A = ½ ab sinθ where a and b are the sides and θ is the contained angle.
Now, to maximize the are of the triangle, we need to find it's critical points by setting A' = 0
A' = ½ ab cosθ
0 = ½ ab cosθ
θ = π/2
Thus at angle θ = π/2, the area of the triangle is at it's maximum