Question

which expressions can be used to find m∠abc? choose two correct answers. cos⁻¹(9.8/8.3) cos⁻¹(7.5/9.8) sin⁻¹(7.5/9.8) sin⁻¹(9.8/7.5)

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, for an acute angle $\theta$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $ABC$ with right - angle at $C$, for $\angle ABC$, the opposite side to $\angle ABC$ is $AC = 7.5$ in, the adjacent side is $BC=6.3$ in, and the hypotenuse is $AB = 9.8$ in.

Step2: Calculate $\sin\angle ABC$ and $\cos\angle ABC$

$\sin\angle ABC=\frac{AC}{AB}=\frac{7.5}{9.8}$, so $\angle ABC=\sin^{- 1}(\frac{7.5}{9.8})$. Also, $\cos\angle ABC=\frac{BC}{AB}=\frac{6.3}{9.8}$, so $\angle ABC=\cos^{-1}(\frac{6.3}{9.8})$.

Answer:

$\cos^{-1}(\frac{6.3}{9.8})$, $\sin^{-1}(\frac{7.5}{9.8})$