Question

prove that : cos30°=root3÷2​

Answer 1

For this,

Let us consider an Equilateral triangle ABC and AD is perpendicular to BC.

Let AB = 2a, BC = 2a and AC = 2a

As we know that, each angle of Equilateral triangle is 60°. And perpendicular divides into two right angled triangle.

By Pythagoras Theorum.

In triangle ADC.

=> AD^2 = AC^2 - DC^2

=> AD^2 = (2a)^2 - (a)^2

=> AD^2 = 4a^2 - a^2

=> AD^2 = 3a^2

$=>AD=\sqrt{3{a}^{2}}$

$=> AD = \sqrt{3a}$

As we know that,

=> Cos= B/H

$=> Cos = \frac{\sqrt{3a}}{2a}$

$=> Cos= \frac{\sqrt{3}}{2}$

$\bold{Hence\:\: Proved}$