Question

using the inverse of the tangent ratio to find the approximate angle measure at vertex b. round your answer to the nearest whole degree

Explanation:

Step1: Recall tangent ratio formula

In right - triangle \(ABC\) with right - angle at \(C\), \(\tan B=\frac{AC}{BC}\). Here, \(AC = 25\) and \(BC = 20\), so \(\tan B=\frac{25}{20}=\frac{5}{4}=1.25\).

Step2: Use inverse tangent function

We know that if \(\tan B = x\), then \(B=\arctan(x)\). So \(B=\arctan(1.25)\).
Using a calculator, \(B=\arctan(1.25)\approx51.34^{\circ}\).

Step3: Round to nearest whole degree

Rounding \(51.34^{\circ}\) to the nearest whole degree gives \(51^{\circ}\).

Answer:

\(51^{\circ}\)