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Question

In ΔABC, A=60,B=45 and AB= 10cm as shown in the figure. Then find the area of the triangle.


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Solution

In given ΔABC,

Draw CD perpendicular to AB

DCB=180(90+45)=45

In right angled triangle BDC

tan 45=CDDB=1

So, CD=DB=x

In right angled triangle ADC

tan 60=CDAD

3=xADAD=x3

AB=AD+DB

10=x3+x

x(13+1)=10

x3+13=10

x=1033+1

Area =12×AB×CD

=12×10×x

=12×10×103(3+1)

=5033+1×(31)(31)=503(31)2=25(33)cm2


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