Question

∠b =
round your answer to the nearest hundredth.
you might need: calculator
show calculator

Explanation:

Step1: Identify the trigonometric ratio

Since we know the adjacent side ($AC = 5$) and the opposite side ($BC=6$) to $\angle B$ in right - triangle $ABC$, we use the tangent function. $\tan B=\frac{AC}{BC}$.

Step2: Calculate the value of $\tan B$

$\tan B=\frac{5}{6}\approx0.8333$.

Step3: Find the angle $B$

We use the inverse - tangent function, $B = \arctan(0.8333)$. Using a calculator, $B=\arctan(0.8333)\approx39.81^{\circ}$.

Answer:

$39.81$