Question

10 trigonometric ratios and functions exam
determine the measure of angle c using a trigonometric ratio.
a) 34.85°
b) 0.01°
c) 29.74°
d) 55.15°

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle $ABC$ with right - angle at $A$, we know the opposite side to angle $C$ is $AB = 16$ and the hypotenuse is $BC=28$. We use the sine ratio $\sin C=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin C=\frac{AB}{BC}=\frac{16}{28}=\frac{4}{7}$.

Step2: Find the angle measure

We know that if $\sin C=\frac{4}{7}$, then $C = \sin^{- 1}(\frac{4}{7})$. Using a calculator, $C=\sin^{-1}(\frac{4}{7})\approx29.74^{\circ}$.

Answer:

C. $29.74^{\circ}$