Find the value of sin 60° geometrically?
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Answer:
⇒ Draw an equilateral △ABC
⇒ In △ADB,∠D=90
o
⇒ Let a be the side of equilateral triangle.
∴ AB=BC=AC=a
⇒ AB
2
=AD
2
+BD
2
⇒ a
2
=AD
2
+(
2
a
)
2
⇒ AD
2
=a
2
−(
2
a
)
2
⇒ AD
2
=a
2
−
4
a
2
⇒ AD
2
=
4
3a
2
∴ AD=
2
3
a
⇒ sin60
o
=
Hypotenuse
Opp.side
=
BD
AD
=
a
2
3
a
∴ sin60
o
=
2
3
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