In the formula `angleA+angleB+angleC=180^(@)`, if `angleA=90^(@)` and `angle B=55^(@)`, then `angleC=`_______

Options

A. `pi//4`
B. `pi//6`
C. `pi//3`
D. none of these

Answer

3

Explanation

`b cos theta =a or b cos theta +b=4`
or `b=(4)/(1+cos theta)`
`thereforea=(4costheta)/(1+costheta)`
or Area =`triangle=1/2 ba sin theta`
`=1/2 (4)/(1+cos theta)(4cos theta)/(1+cos theta)xxsin theta=(4sin 2 theta)/(1+cos theta)`
`therefore (d triangle)/(dtheta)=4(2 cos 2 theta)(1+cos theta)^(2)+2sin 2 theta(1+cos theta)(sin theta)/(1+cos theta)^(4)`
or `cos 2 theta + cos theta =0 or cos 2 theta )+sin 2 theta = cos (pi-theta)`
or `theta =(pi)/(3)`
Therefore `triangel` is maximum when when `theta =(pi)/(3)`