Question

Trig - law of sines question, that has frustrated me.

Answer 1

You want to know how the law of sines applies here?

Answer 2

Sure.

Answer 3

Well, consider first the point D, located where s and BA intersect.

Answer 4

Go on

Answer 5

sin(mCDB) / a = sin(B) / s = sin(x) / BD

Answer 6

sin(mCDA) / a = sin(A) / s = sin(x) / AD

Answer 7

BA = BD + AD
mCDB + mCDA = 180

Answer 8

Change that one equation to:
sin(mCDA) / b = sin(A) / s = sin(x) / AD

Answer 9

I guess you just use algebra from here on out.

Answer 10

"sin(mCDA) / a = sin(A) / s = sin(x) / AD"

was that a ^^^ meant to be a b?

Answer 11

Yep, that is what I meant when I make recent correction

Answer 12

Ah, yeah i prob just got lazy. Still cbf finishing it off.. I just thought i was missing something that'd make it easier/quicker.

Answer 13

Assume angle bisector intersects AB at D.

Triangle CBD: s / sin(B) = BD / sin(x) ; BD = s * sin(x) / sin(B) ---- (1)
Triangle CAD: s/ sin(A) = DA / sin(x) ; DA = s * sin(x) / sin(A) ---- (2)
Triangle CBA: a / sin(A) = b / sin(B) = c / sin(2x) from which we get:
1 / sin(A) = c / ( a * sin(2x) ) ---- (3) and
1 / sin(B) = c / ( b * sin(2x) ) ---- (4)

Add (1) and (2):
BD + DA = s * sin(x) * ( 1 / sin(B) + 1 / sin(A) ) or
c = s * sin(x) * ( 1 / sin(B) + 1 / sin(A) ). Substitute (3) and (4):
c = s * sin(x) * ( c / (b * sin(2x)) + c / ( a * sin(2x)) )
c = s * sin(x) * c / sin(2x) * ( 1 / b + 1 / a )
1 = s * sin(x) * 1 / sin(2x) * (a+b) / ab
s = ab * sin(2x) / ( (a+b) * sin(x) )
s = ab * 2 * sin(x) * cos(x) / ( (a+b) * sin(x) )

s = 2abcos(x) / (a+b)

Answer 14

Thanks @ranga, that's what I figured... i just kept thinking i was missing something that'd cut down the work (usually the difficult problems in the book I teach from don't take that much effort).

Answer 15

You are welcome! You teach at school/university and tutor?

Answer 16

Yeah, teach at a high school. This was one of the hwk problems i assigned lol (didn't think it looked that much work), then got frustrated trying to do it myself when a couple of students asked me about it.

Answer 17

cool. math and physics teacher?

Answer 18

Yep :)

Answer 19

Alright. Two great subjects to teach.

Answer 20

Indeed! They are fun!

Answer 21

Oops, bumped by accident.

Answer 22

i was thinking about becoming a high school teacher too but after being a tutor at a university for a year, I realized I never liked kids! XD they're annoying sometimes.