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Trigonometry> solution of triangles...

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if the bisector of angle A of ΔABC makes an angle Φ wid BC, then sinΦ is equal to....?

nishant kumar agarwal , 15 Years ago

Grade Upto college level

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Hello student, please find answer to your question
Let the bisector of angle A touch the side BC at D.
ADC & ADB form a a triangle
Apply sine rule,
$\frac{sin\phi }{b} = \frac{sin\frac{A}{2}}{DC}$
$\frac{sin(180-\phi) }{c} = \frac{sin\frac{A}{2}}{BD}$
$\frac{sin(\phi) }{c} = \frac{sin\frac{A}{2}}{BD}$
$BD + DC = \frac{sin(\frac{A}{2})[b+c]}{sin(\phi )}$
$a = \frac{sin(\frac{A}{2})[b+c]}{sin(\phi )}$
$sin(\phi ) = \frac{sin(\frac{A}{2})[b+c]}{a}$

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