sin30° value?

sin 30° = 0.5

Why the value is 0.5

In a right‑angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse:

\[ \sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} \]

Consider an equilateral triangle of side 1 unit. Each interior angle is 60°. If we drop a perpendicular from one vertex to the opposite side, we split the triangle into two 30°‑60°‑90° right triangles.

1. The hypotenuse of each right triangle is the original side = 1.
2. The side opposite the 30° angle is half the base = \(\frac{1}{2}\).
3. Thus \(\displaystyle \sin30° = \frac{\frac{1}{2}}{1} = \frac{1}{2}=0.5.\)

Common exam tip

Remember the special angles table: \(\sin30° = \frac{1}{2},\; \cos30° = \frac{\sqrt3}{2},\; \tan30° = \frac{1}{\sqrt3}\). A frequent mistake is to confuse \(\sin30°\) with \(\sin60°\); the latter equals \(\frac{\sqrt3}{2}\), not 0.5.