What is the exact value of sin 30° ? Enter your answer, as a simplified fraction

Solution:

Consider an equilateral triangle ABC

We know that each angle in an equilateral triangle is 60^°

∠A = ∠B = ∠C = 60^°

Construct a perpendicular line AD from A to the side BC

ΔABD ≅ ΔACD

As BD = DC ∠BAD = ∠CAD

We see that the ΔABD is a right triangle which is right-angled at D

∠BAD = 30^° and ∠ABD = 60^°

To find the trigonometric ratios we should know the lengths of sides of the triangle.

Consider AB = 2a

BD = 1/2 BC = a

In order to find the value of sin 30° let us make use of the sine formula

Sin 30° = opposite side/hypotenuse side

Substituting the values

Sin 30° = BD/AB = a/2a = 1 / 2

Therefore, the exact value of sin 30° is 1/2.

What is the exact value of sin 30° ? Enter your answer, as a simplified fraction

Summary:

The exact value of sin 30° is 1/2.