Find the value if sin60° geometrically
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Joshuawoskk:
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consider an equilateral triangle ABC with AB=BC=CA=2a
∠A=∠B=∠C=60
draw AD perpendicular to BC
In ABD and ACD
AD=AD [Common]
∠ADB =∠ADC [90]
AB=AC [EQUILATERAL TRIANGLE]
△ABC ≅ △ACD [RHS congruence]
BD=DC [ CPCT ]
∠BAD=∠CAD
BD=2a/2=a
∠BAD=60/2=30
In a triangle ABD,apply pythogras therom to get
AD = √3a
In triangle ABD
Sin 60 =AD/AB
=√3a/2a
=√3/2
∠A=∠B=∠C=60
draw AD perpendicular to BC
In ABD and ACD
AD=AD [Common]
∠ADB =∠ADC [90]
AB=AC [EQUILATERAL TRIANGLE]
△ABC ≅ △ACD [RHS congruence]
BD=DC [ CPCT ]
∠BAD=∠CAD
BD=2a/2=a
∠BAD=60/2=30
In a triangle ABD,apply pythogras therom to get
AD = √3a
In triangle ABD
Sin 60 =AD/AB
=√3a/2a
=√3/2
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