Question

what is ( mangle b ) to the nearest tenth?

( mangle b=) 。

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan B=\frac{opposite}{adjacent}\). Here, the side opposite to \(\angle B\) is \(AC = 14.1\) and the side adjacent to \(\angle B\) is \(BC=22.9\). So, \(\tan B=\frac{14.1}{22.9}\).

Step2: Calculate \(\tan B\)

\(\tan B=\frac{14.1}{22.9}\approx0.6157\).

Step3: Find the angle \(B\)

We know that \(B = \arctan(0.6157)\). Using a calculator, \(B=\tan^{- 1}(0.6157)\approx31.6^{\circ}\).

Answer:

\(31.6\)