Question

In a ∆ABC, 12AngleA = 20AngleB, also Angle B and C are divided by OB and OC, such that Angle OBC : ABO = ( greater root : Smaller root) of the equation ( x² - 3x + 2 = 0 ) and Angle ACO : BCO = area bounded by x- axis , y- axis, x = z and y = 10) : ( area bounded by x- axis , y-axis and ( -y = x - 10). Show all the results.​

Answer 1

By Pythagoras theorem, we have 

AC2=AB2+BC2

TRIGONOMETRICRATIOS

⇒AC2=122+52

⇒AC2=169

⇒AC=13

When we consider t-ratios of ∠C, we have 

Base = BC = 5, Perpendicular = AB = 12 and, Hypotenuse = AC = 13

∴cosC=HypotenuseBase=135andcotC=PerpendicularBase=PerpendicularBase=125