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=1/2*ab*sin*theta.*
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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

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