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 \(ABC\), we know the adjacent side to angle \(A\) (\(AC = 27\) m) and the hypotenuse (\(AB = 47\) m). We use the cosine ratio \(\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos A=\frac{27}{47}\).

Step2: Use inverse cosine

To find angle \(A\), we use the inverse - cosine function. \(A=\cos^{- 1}(\frac{27}{47})\).

Step3: Calculate the value

Using a calculator, \(\cos^{-1}(\frac{27}{47})\approx54.9^{\circ}\).

Step4: Round the answer

Rounding \(54.9^{\circ}\) to the nearest whole number, we get \(55^{\circ}\).

Answer:

\(55\)