Question

round your answer to the nearest hundredth.
triangle diagram: right angle at c, bc = 6, angle at b = 40°, ac = ? (labeled with ?), vertices a, b, c

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\) (right - angled at \(C\)), we know that \(\tan B=\frac{AC}{BC}\). We are given that \(BC = 6\) and \(\angle B=40^{\circ}\).

Step2: Solve for \(AC\)

From \(\tan B=\frac{AC}{BC}\), we can re - arrange the formula to get \(AC = BC\times\tan B\). Substitute \(BC = 6\) and \(B = 40^{\circ}\) into the formula. We know that \(\tan(40^{\circ})\approx0.8391\). So \(AC=6\times\tan(40^{\circ})\approx6\times0.8391 = 5.0346\).

Step3: Round to nearest hundredth

Rounding \(5.0346\) to the nearest hundredth, we look at the thousandth place digit which is \(4\). Since \(4\lt5\), we round down. So \(AC\approx5.03\).

Answer:

\(5.03\)