Page 32 - 11-Math-12 Application of Trigonometry

112. .QAupapdlircaattiiconEqofuTartiigoonnsometry eeLLeeaarrnn..PPuunnjjaabb

Similarly, we can prove that

=R =2 sbin b and R R.c
2 sin g

Hence =R =a =b c
2 sina 2 sin b 2 sin g

a) Deduction of Law of Sines:

We know t=hat R =a =b c
2sin a 2sin b 2 sin g

⇒ a =sinb b =sinc g =2R
sin a =sinb b =sinc g , which is the law of sines.

a
∴ sin a

b) Prove that: R = abc
4∆

Proof: We know that: R = a
2sin a

=⇒ R 2 .2 sinaa2=cos a2  sin a 2 sin a cos a 
2 2 

=a
s(s - b)(s - c) s(s - a) (by half angle formulas)
4 bc bc

= abc
4 s(s - a)(s - b)(s - c)

∴ R= abc ( )=∆ s(s - a)(s - b)(s - c)
4∆

version: 1.1

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