Question

Find the value of tan 60 geometrically

Answer 1

Let AC=AB=BC=2a

then AM=a
[why? because AMB and BMC are similar triangles. [you may ask if you get confused again]
means, AM/AC=BM/BC
but as we can see, for equilateral triangles, AC=BC --> AM=BM]
AM=√3a [using Pythagoras theorem]


now, tanA=tan60=3√a/a=3√ --> tan60=√3

Hope it helped.