1: In △ ABC, let Tana / tanb = 2C-B / B, find the value of a? 2: in △ ABC, a + B = 10, COSC is a root of the square of equation 2x - 3x-2 = 0, find the minimum value of perimeter of △ ABC?

1: In △ ABC, let Tana / tanb = 2C-B / B, find the value of a? 2: in △ ABC, a + B = 10, COSC is a root of the square of equation 2x - 3x-2 = 0, find the minimum value of perimeter of △ ABC?

(1) According to the sine theorem, Tana / tanb = 2C-B / B, i.e
Sinacosb / cosasinb = (2sinc SINB) / SINB, i.e
Sinacosb / cosa = 2sinc SINB
Sinacosb = 2sinccosa cosasinb
Sinacosb + cosasinb = 2sinccosa, i.e
Sin (a + b) = 2sinccosa
Sinc = 2sinccosa, so cosa = 1 / 2
So a = 60
(2) COSC is a root of the equation 2x ^ 2-3x-2 = 0, so we can know that COSC = - 1 / 2
The circumference of ABC:
P=a+b+c
=10+c
=10+SQR(a^2+b^2-2abcosC)
=10+SQR(a^2+b^2+ab)
=10+SQR[(a+b)^2-ab]
=10+SQR[100-ab]
AB = 10 + 5sqr (3)
So the minimum perimeter of △ ABC is 10 + 5sqr (3)