Question

use the inverse trigonometric keys on a calculator to find the measure of angle a.
a = (square^{circ}) (round the answer to the nearest whole number.)

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the opposite side to angle \(A\) (\(BC = 31\) m) and the hypotenuse (\(AB=38\) m). The sine of an angle in a right - triangle is defined as \(\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(A)=\frac{31}{38}\).

Step2: Use inverse sine function

To find angle \(A\), we use the inverse - sine function \(A = \sin^{-1}(\frac{31}{38})\).

Step3: Calculate the value

Using a calculator, \(A=\sin^{-1}(\frac{31}{38})\approx54.9^{\circ}\).

Step4: Round the result

Rounding to the nearest whole number, \(A\approx55^{\circ}\).

Answer:

\(55\)