Question

Find the values of sin 30, cos30, tan30 geometrically.
Please answer fast!!!(^_^)

Answer 1

Here we go,

In the diagram, an equilateral triangle ABC is given,


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

Now, here suppose that AB=AC=BC=2a
then AM=BM=a. 

For angle ACM , sinC=sin30=a/2a=1/2 --> sin30=1/2

using Pythagoras theorem, CM=√3a
For angle CAM, sinA=sin60=√3a/2a=√3/2 --> sin60=√3/2

Now, tanC=tan30=a/√3a =1/√3 --> tan30=1/√3

Hope it helped. ^^

Answer 2

sin30=1/2

cos30=sqrt(3)/2

tan30=1/sqrt(3)