Question

1. 24° 12 5.3

Explanation:

Step1: Use the tangent function

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 24^{\circ}$, the adjacent side is $12$, and the opposite side is $x$.

Step2: Set up the equation

We have $\tan(24^{\circ})=\frac{x}{12}$.

Step3: Solve for \(x\)

Since $\tan(24^{\circ})\approx0.4452$, then $x = 12\times\tan(24^{\circ})$.
Substitute the value of $\tan(24^{\circ})$: $x=12\times0.4452 = 5.3424\approx5.3$.

Answer:

$x\approx5.3$