Question

what is the approximate degree measure of angle a in the triangle?

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the opposite side (\(BC = 14\)) and the adjacent side (\(AC = 18\)) to angle \(A\). We use the tangent function: \(\tan(A)=\frac{BC}{AC}\).

Step2: Calculate the tangent value

\(\tan(A)=\frac{14}{18}=\frac{7}{9}\approx0.7778\).

Step3: Find the angle

We use the inverse - tangent function \(A=\tan^{- 1}(0.7778)\). Using a calculator in degree mode, \(A=\tan^{-1}(0.7778)\approx37.9^{\circ}\).

Answer:

37.9