Question

find the missing side.
23
30°
x
x = ?

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle with a 30° angle. The hypotenuse is 23, and we want to find the side opposite the 30° angle. In a right - triangle, the sine of an angle $\theta$ is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\theta = 30^{\circ}$, $\sin(30^{\circ})=\frac{1}{2}$.

Step2: Apply the sine formula

We know that $\sin(30^{\circ})=\frac{x}{23}$. Since $\sin(30^{\circ})=\frac{1}{2}$, we can substitute this value into the equation: $\frac{1}{2}=\frac{x}{23}$.
To solve for $x$, we can cross - multiply. Multiply both sides of the equation by 23: $x = 23\times\frac{1}{2}$.

Step3: Calculate the value of x

$23\times\frac{1}{2}=\frac{23}{2}=11.5$

Answer:

11.5