two sides of a triangle are of length 2A and 2B and they contain an angle of 120 degrees if the angle opposite to the side 2a is theta then tan theta is equal to
Answers
Answered by
43
Heya!!!
Let the opposite side be x...
so sinθ/2a=sin120/x ==> x2 = 3a2/sin2θ ... (i)
now cos120 = [(2a)2 + (2b)2 - x2]/(2*2a*2b)
==> -1/2 = (4a2+4b2-x2)/8ab
==> -4ab = 4a2+4b2-x2
==> x2 = 4a2+4b2 + 4ab ... (ii)
equating (i) and (ii),
sin2θ = 3a2/(4a2+4b2 + 4ab)
==> tan2θ = 3a2/(a2+4b2+4ab) = 3a2/(a+2b)2
==> tanθ = a√3/(a+2b)
Hope this helps you ☺☺
Let the opposite side be x...
so sinθ/2a=sin120/x ==> x2 = 3a2/sin2θ ... (i)
now cos120 = [(2a)2 + (2b)2 - x2]/(2*2a*2b)
==> -1/2 = (4a2+4b2-x2)/8ab
==> -4ab = 4a2+4b2-x2
==> x2 = 4a2+4b2 + 4ab ... (ii)
equating (i) and (ii),
sin2θ = 3a2/(4a2+4b2 + 4ab)
==> tan2θ = 3a2/(a2+4b2+4ab) = 3a2/(a+2b)2
==> tanθ = a√3/(a+2b)
Hope this helps you ☺☺
Similar questions