Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle ABC, we know the opposite side to angle ABC is AC = 10.5 cm and the hypotenuse is AB = 20 cm. We use the sine ratio $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(x)=\frac{AC}{AB}$.

Step2: Substitute values

Substitute AC = 10.5 cm and AB = 20 cm into the sine formula: $\sin(x)=\frac{10.5}{20}=0.525$.

Step3: Find the angle

To find the angle x, we take the inverse - sine of 0.525, i.e., $x = \sin^{- 1}(0.525)$. Using a calculator, $x\approx31.7^{\circ}$.

Answer:

31.7°