MHT CET 2017 Math Solved Paper

(c) We have, sin2A+sin2B = sin2C
⇒ a2+b2=c2 (From Sine rule)
∴ ΔABC is right angled triangle and ∠ACB=90°
So, area of (ΔACB)=

1

2

ab
By Sine rule’s we get

a

sin‌A

=

b

sin‌B

=

c

sin‌C

⇒

a

sin‌A

=

b

sin‌B

=

10

1

Hence, a = 10 sin A
and b = 10 sinB
Area of ΔACB =

1

2

(10 sin A)(10 sin B) [From (i)]
= 50 sin A sinB
As, maximum value of sin A sin B =

1

2

Hence, maximum value of area of ΔACB
= 50 x

1

2

= 25