Grade Upto college levelTrigonometry

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

nishant kumar agarwal

16 Years agoGrade Upto college level

1 Answer

Jitender Singh

12 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,
$\frac{sin\phi }{b} = \frac{sin\frac{A}{2}}{DC}$
$\frac{sin(180-\phi) }{c} = \frac{sin\frac{A}{2}}{BD}$
$\frac{sin(\phi) }{c} = \frac{sin\frac{A}{2}}{BD}$
$BD + DC = \frac{sin(\frac{A}{2})[b+c]}{sin(\phi )}$
$a = \frac{sin(\frac{A}{2})[b+c]}{sin(\phi )}$
$sin(\phi ) = \frac{sin(\frac{A}{2})[b+c]}{a}$