Question

abc is a right angled triangle in which b  90o and c  2a . If bc = 12 cm then ar abc is

Answer 1

We know,

Sum of all angles of a triangle = 180°

Therefore, angle A + angle B + angle C = 180°

angle A + 90° + 2*angle A = 180° [ from question, C = 2A and B = 90°]

3*angle A + 90° = 180°

3*Angle A = 90°

Angle A = 30°

And angle C = 2*angle A = 60°

Using sine formula ,

BC = a , AB = c , and CA = b

So, sin30°/BC = sin60°/AB

(1/2)/12 = (√3/2)/AB

1/24 = √3/2AB

AB = 12√3 cm

Hence, area of ∆ABC = 1/2*BC*AB

= 1/2*12*12√3

= 72√3 cm²