Question

Trigonometric functions of some specific angles with proof

Answer 1

Answer:

Trigonometric Ratios of 30° and 60°

Let ABC be an equilateral triangle whose sides have length a (see the figure given below). Draw AD perpendicular to BC, then D bisects the side BC.

Then,

BD  =  DC  =  a/2

∠BAD  =  ∠DAC  =  30°

Now, in right triangle ADB, ∠BAD  =  30° and BD  =  a/2.

In right triangle ADB, by Pythagorean theorem, 

AB2  =  AD2 + BD2

a2  =  AD2 + (a/2)2

a2 - (a2/4)  =  AD2

3a²/4  =  AD2

√(3a2/4)  =  AD

√3 ⋅ a/2  = m AD 

Step-by-step explanation:

I hope it will helpful to you