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 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.
