If cos(θ) = -2 9 , and 90° < θ < 180°, what is the value of tan(θ)? a) -77sqroot/2 b) -77sqroot/9 c) 77sqroot/2 d) 77sqroot/9 e) 65sqroot/9

We know that

if  90° < θ < 180°
then
θ> belong to the second quadrant
so
tan θ is negative

sin² θ + cos² θ=1> sin² θ=1-cos² θ>sin² θ=1-(-2/9)²
sin² θ=1-(4/81)> 77/81> sin θ=√(77/81)> √77/9
sin θ=(√77)/9

tan θ=sin θ/cos θ> [(√77)/9]/[-2/9]> -√77/2

the answer is the option
A) -77sqroot/2