Question

spiral review • assessment readiness
what is the measure of ∠a?
show hints
28.6°
61.4°
25.6°
0.49°

Explanation:

Step1: Recall the sine - function definition

In right - triangle \(ABC\) with right - angle at \(B\), \(\sin A=\frac{BC}{AC}\). Here, \(BC\) is the side opposite to \(\angle A\) and \(AC\) is the hypotenuse. Given \(BC = 2.2\) and \(AC = 4.6\), so \(\sin A=\frac{2.2}{4.6}\).

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

\(\sin A=\frac{2.2}{4.6}\approx0.4783\).

Step3: Find the angle \(A\)

We know that if \(\sin A = x\), then \(A=\sin^{- 1}(x)\). So \(A=\sin^{-1}(0.4783)\). Using a calculator in degree mode, \(A\approx28.6^{\circ}\).

Answer:

\(28.6^{\circ}\)