In a triangle ABC, AB =20 cm, ∠A=30∘, AC = 18 cm The area of the triangle is equal to _______.
90cm2
Draw CD perpendicular to AB.
In triangle ADC
∠C=30∘.....(Angle sum property)
Hence, all the angles of triangle ADC are :
30∘,60∘,90∘
Now,
The ratios of the sine of angles=sin(30):sin(60):sin(90)
⇒12:√32:1
⇒1:√3:2
So, the sides CD, AD, AC will be in the ratio 1:√3:2, therefore the corresponding sides can be calculated as
30∘60∘90∘1:√3:2CDADAC↓↓↓99√318
So, the perpendicular CD is equal to 9 cm
Area of triangle =12×AB×CD=12×20×9
=90cm2