right triangle xyz has a right angle at vertex y and a hypotenuse that measures 24 cm. angle zxy measures…

Answer:

A. 8.2 cm

Explanation:

Step1: Identify the trig - ratio

In right - triangle XYZ, we know the hypotenuse (c = 24) cm and we want to find the adjacent side (XY) to angle (ZXY=\theta = 70^{\circ}). We use the cosine function: (\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}).

Step2: Set up the equation

Let (XY = x). Then (\cos(70^{\circ})=\frac{x}{24}).

Step3: Solve for (x)

We know that (\cos(70^{\circ})\approx0.342). So, (x = 24\times\cos(70^{\circ})). [x=24\times0.342 = 8.208\approx8.2\text{ cm}]