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Grade: 12
        
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.
3 years ago

Answers : (2)

Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							
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
3 years ago
Vasantha Kumari
askIITians Faculty
38 Points
							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

3 years ago
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