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Question

In Δ ABC, AB=15 cm,  A=30,  B=130. The area of the triangle will be equal to [Tan 30=0.57Tan 50=1.2]



A

 132.8 cm2  

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B

 152.18 cm2  

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C

 122.13 cm2  

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D

 142.12 cm2  

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Solution

The correct option is B

 122.13 cm2  


Draw CD perpendicular to AB extended till D.  

 CBD=180130=50  

 Tan 50=CDBD=hx    

h=x tan 50  

h=1.2x      ...(i)  

In Δ ACD  

Tan 30=CDAD=h(15+x)   

 h=(15+x).Tan 30  

h=(15+x).0.57    

h=8.55+0.57x     from ... (i)

From (i) & (ii) we have  

1.2 x=8.55+0.57 x    

0.63 x=8.55  

x=13.57  

 h=1.2x  from  ...(i)   

h=1.2×13.57  

 h=16.28  

 Area of triangle ABC =12×AB×h  

=12×15×16.28  

=122.13 cm2


Mathematics

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