Question

In ABC, AB = 6 cm, BC = 8 cm and ∠ABC = 150°. Find the area of ΔABC.

[Hint: Drop AP ⊥ CB extended.]

Answer 1

Given:

In △ABC,

AB = 6 cm

BC = 8 cm

∠ABC = 150°

Step 1:

Extend line CB beyond B.

Drop a perpendicular AP ⊥ CB (extended) from point A.

Height = AP    ... [Consider right triangle ΔABP.]

Step 2: Use Trigonometry to find height AP

In ΔABP,

Angle between AB and base (on extension) is 180° − 1 − 150° = 30°

So, ∠ABP = 30°

sin(30°) = `(AP)/(AB)`

= `1/2 = (AP)/6`

= AP = 3cm

Step 3: 

Area = `1/2` × base × height

= `1/2 xx 8 xx 3`

= 12 cm²