In ΔABC, ∠A=60∘,∠B=45∘ and AB= 10cm as shown in the figure. Then find the area of the triangle.
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=xAD⇒AD=x√3
AB=AD+DB
10=x√3+x
x(1√3+1)=10
x√3+1√3=10
x=10√3√3+1
Area =12×AB×CD
=12×10×x
=12×10×10√3(√3+1)
=50√3√3+1×(√3−1)(√3−1)=50√3(√3−1)2=25(3−√3)cm2