Question

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Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the hypotenuse (12) and we need to find the adjacent side to the \(68^\circ\) angle (x). The cosine function relates adjacent and hypotenuse: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Set up the equation

\(\cos(68^\circ)=\frac{x}{12}\)

Step3: Solve for x

Multiply both sides by 12: \(x = 12\times\cos(68^\circ)\)
Calculate \(\cos(68^\circ)\approx0.3746\), then \(x\approx12\times0.3746 = 4.4952\)

Step4: Round to nearest tenth

\(x\approx4.5\)

Answer:

\(4.5\)