The equation [tex]\boxed{\text{cos}^{-1}\left(\dfrac{11.9}{14.5}\right)=\theta}[/tex] can be used to measure [tex]\angle\text{GFE}[/tex].
Further explanation:
Given:
The value of GF is [tex]14.5[/tex].
The value of EF is [tex]11.9[/tex].
The measurement of [tex]\angle\text{ GEF}[/tex] is [tex]90^{\circ}[/tex].
The measurement of [tex]\angle\text{ GFE}[/tex] is [tex]\theta[/tex].
Calculation:
The [tex]\angle\text{GEF}[/tex] is [tex]90^{\circ}[/tex], it means that the [tex]\triangle\text{ GEF}[/tex] is a right angle triangle.
The hypotenuse of the [tex]\triangle\text{ GEF}[/tex] is GF.
The base of the [tex]\triangle\text{ GEF}[/tex] is EF.
The cosine of the angle [tex]\theta[/tex] is defined as the ratio of the adjacent side of angle [tex]\theta[/tex] and hypotenuse of the [tex]\triangle\text{ GEF}[/tex].
The adjacent side of angle [tex]\theta[/tex] is EF.
[tex]\boxed{\cos\theta=\dfrac{\text{EF}}{\text{GF}}}[/tex] …… (1)
Substitute [tex]11.9[/tex] for EF and [tex]14.5[/tex] for GF in equation (1) to obtain the value of [tex]\theta[/tex] as follows:
[tex]\boxed{\begin{aligned}\cos\theta&=\frac{\text{EF}}{\text{GF}}\\&=\frac{{11.9}}{{14.5}}\end{aligned}}[/tex]
Now obtain the value of [tex]\theta[/tex] by taking inverse.
[tex]\boxed{\begin{aligned}\cos \theta&=\frac{{11.9}}{{14.5}}\\\theta&={\cos ^{ - 1}}\left( {\frac{{11.9}}{{14.5}}} \right)\\\end{aligned}}[/tex]
Further solve the above equation to obtain the value of [tex]\theta[/tex] as follows:
[tex]\begin{aligned}\theta&={\cos^{-1}}\left({\frac{{11.9}}{{14.5}}}\right)\\\theta&={\cos ^{-1}}\left({0.820}\right)\\\end{aligned}[/tex]
Therefore the equation [tex]\boxed{{{\cos}^{-1}}\left({\frac{{11.9}}{{14.5}}}\right)=\theta}[/tex] can be used to measure [tex]\angle\text{GFE}[/tex].
Thus, the equation [tex]\boxed{\text{cos}^{-1}\left(\dfrac{11.9}{14.5}\right)=\theta}[/tex] can be used to measure [tex]\angle\text{GFE}[/tex].
Learn more:
1. Definition of Angle https://brainly.com/question/3413207.
2. Angle https://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.
