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

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

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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