which equation can be used to find the measure of angle gfe?\ncos⁻¹(14.5/11.9)=θ\ncos⁻¹(11.9/14.5)=θ\nsin⁻¹(1…

which equation can be used to find the measure of angle gfe?\ncos⁻¹(14.5/11.9)=θ\ncos⁻¹(11.9/14.5)=θ\nsin⁻¹(11.9/14.5)=θ\nsin⁻¹(14.5/11.9)=θ

which equation can be used to find the measure of angle gfe?\ncos⁻¹(14.5/11.9)=θ\ncos⁻¹(11.9/14.5)=θ\nsin⁻¹(11.9/14.5)=θ\nsin⁻¹(14.5/11.9)=θ

Answer

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 $GEF$ with right - angle at $E$, the hypotenuse $GF = 14.5$ and the side adjacent to angle $\theta=\angle GFE$ is $EF = 11.9$.

Step2: Determine the correct inverse trigonometric function

Since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and here $\text{adjacent}=11.9$ and $\text{hypotenuse}=14.5$, then $\cos\theta=\frac{11.9}{14.5}$. To find $\theta$, we use the inverse cosine function, so $\theta=\cos^{-1}\left(\frac{11.9}{14.5}\right)$.

Answer:

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