Question

give the solved answer fast​

Answer 1

given:AP=2AB

then

BC=AP/4=

if AP equals to x

then BC=x/4=AC

now,

in right angle triangle APC

tan∅=x/4x

tan∅=1/4

also

tan(∅+beta)=x/2x=1/2

(tan∅+tan beta)/(1+tan∅tanbeta)=1/2

put the value of tan∅

2{1/4+tan(beta)}=1-tan(beta)/4

1/2-1=-tan(beta)/4-2tan(bet)

-1/2=-9tan(beta)/4

tan(beta)=2/9

so, option c)