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Question

In Δ ABC, AB=10 cm, A=40, B=80. The area of triangle ABC will be equal to

[tan 40=0.83tan 80=5.6]



A

50.2 cm2

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B

36.14 cm2

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C

44.18 cm2

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D

30.16 cm2

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Solution

The correct option is D

36.14 cm2


In Δ ABC Draw CD perpendicular to AB  

Let CD = h, AD = x , so DB becomes 10- x

In triangle CDB  

tan 80=CDDB=h(10x)  

 h=(10x). tan 80  

h=(10x).(5.6)  

 h=565.6x       ...(i)  

In Δ CAD  

tan 40=CDAD=hx  

 h=x tan 40  

h=0.83 x     ...(ii)  

From (i)  & (ii) we have  

 565.6x=0.83x  

56=6.43x  

x=8.7 cm    

From (ii) h=0.83×8.7  

h=7.22 cm  

Area of triangle ABC    

=12×AB×CD  

=12×10×7.22=36.14 cm2  


Mathematics

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