Question

find value of 30 degree for all trigonometric ratios geometrically ​

Answer 1

Answer:

Let a rotating line OX−→− rotates about O in the anti-clockwise sense and starting from the initial position OX−→− traces out ∠XOY = 30°.

Trigonometrical Ratios of 30°

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Take a point P on OY−→− and draw PA perpendicular to OX−→− Then, ∠OPA = 60°.

Now, produce PA to B such that PA = MB and join OB.

From ∆PMO and ∆QMO we have,

PA = BA,

OA common

and ∠OBP = ∠OPB = 60°

Therefore, ∠POB = 30° + 30° = 60°; which shows that each angel of triangle OPQ is 60° . Hence ∆OPQ is equilateral.