Forwarded from Deleted Account
Let x=ad=bd
Y=cd
9=2(x^2+y^2)
X^2+y^2=9/2
1/โ2=3+y^2-x^2/2โ3y
โ6y=3+y^2-x^2.........@
โ6y=3+y^2-(9/2-y^2)
โ6y=-3/2+2y^2
2โ6y=-3+4y^2
4y^2-2โ6y-3=0
Y=2โ6+-โ24+48/8
=2โ6+-6โ2/8
=2โ6+6โ2/8=โ6+3โ2/4=โ3+3/2โ2
From equation@
Y^2-x^2=โ6y-3
=โ6(3+โ3)-6โ2/2โ2
=3โ6-3โ2/2โ2
=3โ3-3/2
Cosx=6+3โ3-3/2)/2โ6y
=9+3โ3/4โ6y
=3โ3+3/4โ2y
=3(โ3+1)*2โ2/4โ6(โ3+1)
=6โ2/4โ6=3โ2/2โ6=3/2โ3=โ3/2
X=30
Y=cd
9=2(x^2+y^2)
X^2+y^2=9/2
1/โ2=3+y^2-x^2/2โ3y
โ6y=3+y^2-x^2.........@
โ6y=3+y^2-(9/2-y^2)
โ6y=-3/2+2y^2
2โ6y=-3+4y^2
4y^2-2โ6y-3=0
Y=2โ6+-โ24+48/8
=2โ6+-6โ2/8
=2โ6+6โ2/8=โ6+3โ2/4=โ3+3/2โ2
From equation@
Y^2-x^2=โ6y-3
=โ6(3+โ3)-6โ2/2โ2
=3โ6-3โ2/2โ2
=3โ3-3/2
Cosx=6+3โ3-3/2)/2โ6y
=9+3โ3/4โ6y
=3โ3+3/4โ2y
=3(โ3+1)*2โ2/4โ6(โ3+1)
=6โ2/4โ6=3โ2/2โ6=3/2โ3=โ3/2
X=30
Amarkant Kumar
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Let AD= BD = x
Sin45/x = sinฮธ/โ3
sinฮธ*x= โ3/โ2
Now in triangle BCD
Sin(180-ฮธ)/โ6 = sinx/x
Sinฮธ/โ6 = sinx/x
Sinฮธ*x=sinx*โ6
Sinx=โ3/โ2*โ6= 1/2
X= 30ยฐ
Sin45/x = sinฮธ/โ3
sinฮธ*x= โ3/โ2
Now in triangle BCD
Sin(180-ฮธ)/โ6 = sinx/x
Sinฮธ/โ6 = sinx/x
Sinฮธ*x=sinx*โ6
Sinx=โ3/โ2*โ6= 1/2
X= 30ยฐ