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 right triangle \(ABC\) (right - angled at \(C\)), for angle \(A\), the opposite side to angle \(A\) is \(BC = 14\) and the adjacent side to angle \(A\) is \(AC=18\). We use the tangent function, where \(\tan(A)=\frac{\text{opposite}}{\text{adjacent}}=\frac{BC}{AC}\)

Step2: Calculate the value of \(\tan(A)\)

Substitute \(BC = 14\) and \(AC = 18\) into the formula: \(\tan(A)=\frac{14}{18}=\frac{7}{9}\approx0.7778\)

Step3: Find the measure of angle \(A\)

To find angle \(A\), we take the arctangent (inverse tangent) of \(0.7778\). So \(A=\arctan(0.7778)\)
Using a calculator, \(\arctan(0.7778)\approx38.9^{\circ}\)

Answer:

\(38.9\) (corresponding to the option "38.9")