The value of sin 30° is:

To find the value of $\sin 30^\circ$, we can use the properties of a special right-angled triangle: the $30^\circ-60^\circ-90^\circ$ triangle. ### 1. The Geometry Approach Consider an equilateral triangle with side length $2$. If we draw an altitude from one vertex to the opposite side, we split it into two congruent right-angled triangles with angles $30^\circ$, $60^\circ$, and $90^\circ$. - The **Hypotenuse** of this triangle is $2$. - The **Base** (side opposite $30^\circ$) is half the original side, which is $1$. - The **Altitude** (side opposite $60^\circ$) can be found using the Pythagorean theorem: $1^2 + h^2 = 2^2 \implies h = \sqrt{3}$. ### 2. Definition of Sine The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: $$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$$ ### 3. Calculation For $\theta = 30^\circ$: - Opposite side = $1$ - Hypotenuse = $2$ Substituting these values: $$\sin 30^\circ = \frac{1}{2}$$ Thus, the value of $\sin 30^\circ$ is $1/2$ or $0.5$.