Question

Express the value of tan 30° geometrically

Answer 1

we know that   tan 30° = 1/√3  = √3 / 3   units.

So we will draw a line of length √3 and then trisect that.

Draw a square ABCD of side  1 unit.  Let AB be horizontal line. Join A and C.  AC = √2.

Now draw a line perpendicular to AC at C. Use the geometric tools.  Draw an arc of radius 1 unit to cut this perpendicular at E. Now CE = 1 unit.  Join A and E.  AE equals √3.

Now draw an arc with A as the center and AE as the radius to cut the extended line AB at F.    So AF = √3.

Now use the trisection steps to trisect AF into AG, GH, HF.  Each of them will be equal to 1/√3.

Trisection procedure is standard:

Hope it may help u some how..
Thanks..