Question

∠b =
round your answer to the nearest hundredth.
show calculator

Explanation:

Step1: Use cosine function

In right - triangle \(ABC\) with right - angle at \(C\), \(\cos B=\frac{BC}{AB}\). First, find \(BC\) using the Pythagorean theorem \(BC = \sqrt{AB^{2}-AC^{2}}\). Given \(AC = 8\) and \(AB = 9\), then \(BC=\sqrt{9^{2}-8^{2}}=\sqrt{81 - 64}=\sqrt{17}\).

Step2: Calculate \(\cos B\)

\(\cos B=\frac{\sqrt{17}}{9}\).

Step3: Find the angle

\(B=\cos^{-1}(\frac{\sqrt{17}}{9})\). Using a calculator, \(B=\cos^{-1}(\frac{\sqrt{17}}{9})\approx 62.73^{\circ}\)

Answer:

\(62.73\)