Expert Answer to "Two sides of a triangle have lengths a..." - Plainmath

Daniaal Sanchez

Answered question

2021-10-10

Two sides of a triangle have lengths a and b, and the angle between them is 0. What value of 0 will maximize the triangle's area? [Hint:

A = (\frac{1}{2}) a b \sin 0

]

Answer & Explanation

tabuordg

Skilled2021-10-11Added 99 answers

Since

A (0) = \frac{1}{2} a b \sin 0

using derivatives, we obtain

A^{'} (0) = \frac{1}{2} a b {(\sin 0)}^{'} = \frac{1}{2} a b \cos 0

So,

A^{'} (0) = 0 \Leftrightarrow \cos 0 = 0

Since

0 \in [0^{\circ}, 180^{\circ}] \Rightarrow 0 = 90^{\circ}

Result:

90^{\circ}

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