Question

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bc =
round your answer to the nearest hundredth.
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Explanation:

Step1: Identify trigonometric relation

In right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), \(\cos B=\frac{BC}{AB}\). Given \(AB = 6\) and \(\angle B=35^{\circ}\).

Step2: Calculate \(BC\)

We know that \(BC = AB\times\cos B\). Substitute \(AB = 6\) and \(\angle B = 35^{\circ}\) into the formula. Using a calculator, \(\cos(35^{\circ})\approx0.8192\), so \(BC=6\times\cos(35^{\circ})\approx6\times0.8192 = 4.9152\).

Step3: Round the result

Rounding \(4.9152\) to the nearest hundredth gives \(4.92\).

Answer:

\(4.92\)