Question

6.8 cm 7.5 cm 14.5 cm 17.7 cm

Explanation:

Step1: Use cosine function

In right - triangle \(ABC\) with \(\angle A = 65^{\circ}\) and hypotenuse \(AB = 18\mathrm{cm}\), and we want to find the adjacent side \(x\) to \(\angle A\). The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos A=\frac{x}{AB}\).

Step2: Substitute values

We know that \(A = 65^{\circ}\) and \(AB = 18\mathrm{cm}\). Then \(x = AB\times\cos A\). Since \(\cos65^{\circ}\approx0.4226\), and \(AB = 18\mathrm{cm}\), we have \(x=18\times0.4226 = 7.6068\approx7.5\mathrm{cm}\).

Answer:

\(7.5\mathrm{cm}\)