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Two sides of a triangle have lengths ‘a’ and ‘b’ and the angle between them is (theta).what value of (theta) will maximize the area of the triangle? Find the maximum area of the triangle also.

Two sides of a triangle have lengths ‘a’ and ‘b’ and the angle between them is (theta).what value of (theta) will maximize the area of the triangle? Find the maximum area of the triangle also.

Grade:12

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
Notice that, since 0 < sin? <= 1 for 0° < ? <= 90°:
(1/2)ab(0) < (1/2)absin? <= (1/2)ab(1)
==> 0 < (1/2)absin? <= (1/2)ab.

maximum area is (1/2)ab
when ?=90
Vasantha Kumari
askIITians Faculty 38 Points
9 years ago
We know that the area of a triangle with sides ‘a’ and ‘b’ is A = ½ abcosq.

If we consider A’ to be maximum area of the triangle then the angle is 90° or ½ abcosq = 0.

i.e., when q =90°, the triangle has maximum area.(triangle is a right triangle)

The condition is opposite for minimum area, cosq =90° or angle q =0°.

Thanks & Regards,

Vasantha Sivaraj,

askIITians faculty

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