Subjects geometry

Cos Sin Tan B C2Bc84

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1. Given that \(\triangle XYZ \sim \triangle ACB\), corresponding angles are equal, so angle \(B\) in \(\triangle ACB\) corresponds to angle \(Y\) in \(\triangle XYZ\). 2. In \(\triangle XYZ\), the sides are: \(ZX = 14.4\), \(XY = 16.5\), and hypotenuse \(ZY = 21.9\). 3. Since angle \(Y\) is opposite side \(ZX\) and adjacent to side \(XY\), we find: $$\cos B = \cos Y = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{XY}{ZY} = \frac{16.5}{21.9} \approx 0.75$$ $$\sin B = \sin Y = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{ZX}{ZY} = \frac{14.4}{21.9} \approx 0.66$$ $$\tan B = \tan Y = \frac{\text{opposite}}{\text{adjacent}} = \frac{ZX}{XY} = \frac{14.4}{16.5} \approx 0.87$$ 4. Rounded to the nearest hundredth: $$\cos B \approx 0.75$$ $$\sin B \approx 0.66$$ $$\tan B \approx 0.87$$