Question

∠a =
round your answer to the nearest hundredth.
show calculator

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the opposite side \(BC = 6\) to \(\angle A\) and the hypotenuse \(AB=7\). We use the sine function, \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin A=\frac{BC}{AB}=\frac{6}{7}\).

Step2: Find the angle

To find \(\angle A\), we take the inverse sine of \(\frac{6}{7}\), i.e., \(A = \sin^{- 1}(\frac{6}{7})\).
Using a calculator, \(A=\sin^{-1}(\frac{6}{7})\approx58.999^{\circ}\approx59.00^{\circ}\).

Answer:

\(59.00\)