Question

you might need: calculator
∠a =
round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with right - angle at \(C\), we know the opposite side (\(BC = 6\)) and the hypotenuse (\(AB = 8\)) with respect to angle \(A\). We use the sine ratio \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin A=\frac{BC}{AB}\)

Step2: Substitute the values

Substitute \(BC = 6\) and \(AB = 8\) into the sine formula.
\(\sin A=\frac{6}{8}=\frac{3}{4}= 0.75\)

Step3: Find the angle

To find angle \(A\), we take the inverse sine of \(0.75\), i.e., \(A=\sin^{- 1}(0.75)\).
Using a calculator, \(A=\sin^{-1}(0.75)\approx48.59^{\circ}\)

Answer:

\(48.59\)