Question

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Explanation:

Step1: Identify the trigonometric ratio

We know the hypotenuse (\(20\)) and we need to find the adjacent side (\(x\)) to the angle \(48^{\circ}\). The cosine ratio is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Substitute the values into the formula

Given \(\theta = 48^{\circ}\), hypotenuse \(= 20\), and adjacent \(=x\). So, \(\cos(48^{\circ})=\frac{x}{20}\).

Step3: Solve for \(x\)

Multiply both sides by \(20\): \(x = 20\times\cos(48^{\circ})\). Using a calculator, \(\cos(48^{\circ})\approx0.6691\). Then \(x\approx20\times0.6691 = 13.382\approx13.4\)

Answer:

\(x\approx13.4\)