Question

ac =
round your answer to the nearest hundredth.
b
25°
5
c ? a
show calculator

Explanation:

Step1: Identify trigonometric relation

In right - triangle \(ABC\) with right - angle at \(C\), we know \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 25^{\circ}\), the adjacent side to \(\angle B\) is \(BC = 5\) and the opposite side is \(AC\). So, \(\tan B=\tan(25^{\circ})=\frac{AC}{BC}\).

Step2: Solve for \(AC\)

Since \(BC = 5\) and \(\tan(25^{\circ})\approx0.4663\), and \(\tan(25^{\circ})=\frac{AC}{5}\), then \(AC = 5\times\tan(25^{\circ})\).
\[AC=5\times0.4663 = 2.3315\]

Step3: Round the answer

Rounding \(2.3315\) to the nearest hundredth gives \(2.33\).

Answer:

\(2.33\)