SOH CAH TOA is a mnemonic used to remember the definitions of the three basic trigonometric ratios for a right-angled triangle. Consider a right-angled triangle with an angle $\theta$: ` /| / | / | Opposite / | /____| Hypotenuse Adjacent ` • SOH: Sine = Opposite / Hypotenuse $$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$ • CAH: Cosine = Adjacent / Hypotenuse $$ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} $$ • TOA: Tangent = Opposite / Adjacent $$ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} $$ --- Now, let's solve for $x$ using the previous problem's context: Step 1: Identify the knowns and unknowns from the problem. The given angle is $\theta = 30^\circ$. The side opposite the $30^\circ$ angle is $x$. The hypotenuse is $10$. Step 2: Choose the appropriate trigonometric ratio. Since we have the Opposite side and the Hypotenuse, we use the Sine ratio (SOH). $$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $$ Step 3: Substitute the values into the formula. $$ \sin(30^\circ) = \frac{x}{10} $$ Step 4: Solve for $x$. We know that $\sin(30^\circ) = 0.5$. $$ 0.5 = \frac{x}{10} $$ Multiply both sides by 10: $$ x = 0.5 \times 10 $$ $$ x = 5 $$ The value of $x$ is $\boxed{5}$.