Question

what is the approximate degree measure of angle a in the triangle below? 37.9 38.9 51.1 52.1

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for angle \(A\), the opposite side \(BC = 14\) and the adjacent side \(AC=18\). We use the tangent ratio: \(\tan A=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan A=\frac{14}{18}\).

Step2: Simplify the ratio

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

Step3: Find the angle using the inverse tangent function

\(A = \tan^{-1}(0.7778)\). Using a calculator, \(A\approx37.9^{\circ}\).

Answer:

\(37.9\) (the first option)