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Question

In a triangle ABC, AB =20 cm, A=30, AC = 18 cm The area of the triangle is equal to _______.


A

36cm2

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B

90cm2

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C

48cm2

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D

64cm2

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Solution

The correct option is B

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

3060901:3:2CDADAC99318

So, the perpendicular CD is equal to 9 cm

Area of triangle =12×AB×CD=12×20×9

=90cm2


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