Trigonometry would help with this question.
The area of a regular hexagon is ((3√3)s^2)/2 where s is the side.
Plugging in 2 gives us 6√3 or 10.39 feet.
Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:
<h3>What is the trigonometric identity using in this problem?</h3>
The identity that relates the sine squared and the cosine squared of the angle, as follows:
![\sin^{2}{\theta} + \cos^{2}{\theta} = 1](https://tex.z-dn.net/?f=%5Csin%5E%7B2%7D%7B%5Ctheta%7D%20%2B%20%5Ccos%5E%7B2%7D%7B%5Ctheta%7D%20%3D%201)
In this problem, we have that the sine is given by:
![\sin{\theta} = \frac{1}{3}](https://tex.z-dn.net/?f=%5Csin%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
Hence, applying the identity, the cosine is given as follows:
![\cos^2{\theta} = 1 - \sin^2{\theta}](https://tex.z-dn.net/?f=%5Ccos%5E2%7B%5Ctheta%7D%20%3D%201%20-%20%5Csin%5E2%7B%5Ctheta%7D)
![\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2](https://tex.z-dn.net/?f=%5Ccos%5E2%7B%5Ctheta%7D%20%3D%201%20-%20%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E2)
![\cos^2{\theta} = 1 - \frac{1}{9}](https://tex.z-dn.net/?f=%5Ccos%5E2%7B%5Ctheta%7D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B9%7D)
![\cos^2{\theta} = \frac{8}{9}](https://tex.z-dn.net/?f=%5Ccos%5E2%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
![\cos{\theta} = \pm \sqrt{\frac{8}{9}}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B8%7D%7B9%7D%7D)
![\cos{\theta} = \pm \frac{2\sqrt{2}}{3}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B3%7D)
The tangent is given by the sine divided by the cosine, hence:
![\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csin%7B%5Ctheta%7D%7D%7B%5Ccos%7B%5Ctheta%7D%7D)
![\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cpm%20%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B3%7D%7D)
![\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Cfrac%7B1%7D%7B2%5Csqrt%7B2%7D%7D%20%5Ctimes%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%7D)
![\tan{\theta} = \pm \frac{\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D)
More can be learned about trigonometric identities at brainly.com/question/24496175
#SPJ1
Your answer would be the first one because a reflection is when the object is facing itself
The red corner should face itself
Hope This Helps! :)
Answer:
A reflection in the line y = -2, then a translation 2 units right.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Rigid transformation are transformation that preserves the shape and size of the object. Rotation, reflection, translation are rigid transformation whereas dilation is not a rigid transformation.
Any transformation regarding dilation changes the side length of the object and hence the area.
From the question, only one option is right. The rest options are not right because they involve dilation. The correct option is:
A reflection in the line y = -2, then a translation 2 units right.