Question

which equation can be used to find the measure of angle gfe? $\cos^{-1}\left(\frac{14.5}{11.9}\
ight)=\theta$ $\cos^{-1}\left(\frac{11.9}{14.5}\
ight)=\theta$ $\sin^{-1}\left(\frac{11.9}{14.5}\
ight)=\theta$ $\sin^{-1}\left(\frac{14.5}{11.9}\
ight)=\theta$

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For angle \(\theta=\angle GFE\), the hypotenuse \(GF = 14.5\), the side opposite to \(\theta\) is \(GE\) (not given), and the side adjacent to \(\theta\) is \(FE=11.9\).

Step2: Apply cosine ratio

\(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{FE}{GF}\). Substituting \(FE = 11.9\) and \(GF=14.5\), we get \(\theta=\cos^{-1}(\frac{11.9}{14.5})\)

Answer:

\(\cos^{-1}(\frac{11.9}{14.5})=\theta\) (the second option)