Question

Which equation can be used to find the measure of angle GFE?

Answer 1

The equation $\boxed{\text{cos}^{-1}\left(\dfrac{11.9}{14.5}\right)=\theta}$ can be used to measure $\angle\text{GFE}$.

Further explanation:

Given:

The value of GF is $14.5$.

The value of EF is $11.9$.

The measurement of $\angle\text{ GEF}$ is $90^{\circ}$.

The measurement of $\angle\text{ GFE}$ is $\theta$.

Calculation:

The $\angle\text{GEF}$ is $90^{\circ}$, it means that the $\triangle\text{ GEF}$ is a right angle triangle.

The hypotenuse of the $\triangle\text{ GEF}$ is GF.

The base of the $\triangle\text{ GEF}$ is EF.

The cosine of the angle $\theta$ is defined as the ratio of the adjacent side of angle $\theta$ and hypotenuse of the $\triangle\text{ GEF}$.

The adjacent side of angle $\theta$ is EF.

$\boxed{\cos\theta=\dfrac{\text{EF}}{\text{GF}}}$      …… (1)

Substitute $11.9$ for EF and $14.5$ for GF in equation (1) to obtain the value of $\theta$ as follows:

$\boxed{\begin{aligned}\cos\theta&=\frac{\text{EF}}{\text{GF}}\\&=\frac{{11.9}}{{14.5}}\end{aligned}}$

Now obtain the value of $\theta$ by taking inverse.

$\boxed{\begin{aligned}\cos \theta&=\frac{{11.9}}{{14.5}}\\\theta&={\cos ^{ - 1}}\left( {\frac{{11.9}}{{14.5}}} \right)\\\end{aligned}}$

Further solve the above equation to obtain the value of $\theta$ as follows:

$\begin{aligned}\theta&={\cos^{-1}}\left({\frac{{11.9}}{{14.5}}}\right)\\\theta&={\cos ^{-1}}\left({0.820}\right)\\\end{aligned}$

Therefore the equation $\boxed{{{\cos}^{-1}}\left({\frac{{11.9}}{{14.5}}}\right)=\theta}$ can be used to measure $\angle\text{GFE}$.

Thus, the equation $\boxed{\text{cos}^{-1}\left(\dfrac{11.9}{14.5}\right)=\theta}$ can be used to measure $\angle\text{GFE}$.

Learn more:

1. Definition of Angle brainly.com/question/3413207.

2. Angle brainly.com/question/1953744

Answer details:

Grade: High school

Subject: Mathematics

Chapter:Trigonometry

Keywords:  cos^{-1}( 11.9/14.5)=theta, theta=cos ^{-1}(0.820), Angle, Equation, Triangle, hypotenuse, Base, adjacent,  cosine, trigonometry, right angle Triangle, Measure.

Answer 2

the complete question is

Which equation can be used to find the measure of angle GFE?

cos−1[14.5/11.9 ]= θ

cos−1[11.9/14.5] = θ

sin−1[11.9/14.5] = θ

sin−1[14.5 /11.9]= θ

we know that

in the right triangle FGE

cos θ=adjacent side angle θ /hypotenuse

adjacent side angle θ=FE---------> $11.9$

hypotenuse=FG--------> $14.5$

so

cos θ=$\frac{11.9}{14.5}$

θ=arc cos($\frac{11.9}{14.5}$)

therefore

the answer is the option

cos−1[$\frac{11.9}{14.5}$] = θ