Question

trigonometry. which is the best approximation for the measure of angle abc? 62.3°, 31.7°, 58.3°, 27.7°.

Explanation:

Step1: Recall trigonometric ratio

We use the sine - ratio in right - triangle \(ABC\). \(\sin\angle ABC=\frac{AC}{AB}\). Given \(AC = 10.5\) cm and \(AB = 20\) cm.

Step2: Calculate the sine value

\(\sin\angle ABC=\frac{10.5}{20}=0.525\).

Step3: Find the angle

We know that if \(\sin\theta = 0.525\), then \(\theta=\sin^{- 1}(0.525)\). Using a calculator, \(\theta\approx31.7^{\circ}\).

Answer:

\(31.7^{\circ}\)