Question

∠b =
round your answer to the nearest hundredth.

Explanation:

Step1: Recall tangent function

In right - triangle $ABC$ with right - angle at $C$, $\tan B=\frac{AC}{BC}$. Here, $AC = 4$ and $BC = 7$.

Step2: Calculate tangent value

$\tan B=\frac{4}{7}\approx0.5714$.

Step3: Find the angle

$B=\arctan(0.5714)$. Using a calculator, $B\approx29.74^{\circ}$.

Answer:

$29.74$