Question

What is the exact value of cos 30° ?

Answer 1

Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.

Side AB will be the hypotenuse.

cos 60° = AC / AB                 -------[ cos 60° = 1/2]

So, AB = 2 AC   -------------------------------(1)

Apply Pythagorean Theorem to find BC

AB² = BC² + AC²

4 AC² = BC² + AC²

So,  BC = √3 AC  ------------------------(2)

Now, we shall find the value of cos 30°

cos 30° = CB / AB

or,        =  √3 AC / 2 AC     -------using equations (1) and (2)

So,   cos 30° = √3 / 2

Hence, the exact value of

Since ∠A = 2∠B. So,  cos 30° will be √3 / 2