Question

for angle measures of right triangles which equation can be used to find the measure of angle gfe? sin⁻¹(14.5/11.9)=θ cos⁻¹(11.9/14.5)=θ cos⁻¹(14.5/11.5)=θ sin⁻¹(11.9/14.5)=θ

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $\angle GFE$, the side opposite to it is $GE = 11.9$ and the hypotenuse is $GF=14.5$.

Step2: Use the inverse - sine formula

We know that if $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, then $\theta=\sin^{- 1}(\frac{\text{opposite}}{\text{hypotenuse}})$. Substituting the values, we get $\theta = \sin^{-1}(\frac{11.9}{14.5})$.

Answer:

$\sin^{-1}(\frac{11.9}{14.5})=\theta$ (the fourth option)