$\Delta GHI$ is a right angled triangle.

It is measured that

- Length of the opposite side $\stackrel{\u203e}{GI}$ is $GI=2.5$ meters
- Length of the adjacent side $\stackrel{\u203e}{HI}$ is $HI=4.33$ meters
- Length of the hypotenuse is $\stackrel{\u203e}{HG}$ is $HG=5$ meters
- The angle of the triangle is $\angle GHI={30}^{\xb0}$.

Now, calculate value of the cosine at angle ${30}^{\xb0}$ by considering the length of the adjacent side and length of the hypotenuse.

$cos{30}^{\xb0}=\frac{Length\; of\; the\; Adjacent\; side}{Length\; of\; the\; Hypotenuse}$

$\Rightarrow cos{30}^{\xb0}=\frac{HI}{HG}$

$\Rightarrow cos{30}^{\xb0}=\frac{4.33}{5}$

$\Rightarrow cos{30}^{\xb0}=0.866$

The value of cosine at the angle ${30}^{\xb0}$ is $0.866$ for the triangle $GHI$.

$\Delta FED$ is another right angled triangle and it is measured that,

- The length of the opposite side $\stackrel{\u203e}{DF}$ is $DF=3$ meters
- The length of the adjacent side $\stackrel{\u203e}{EF}$ is $EF=5.196$ meters
- The length of the hypotenuse is $\stackrel{\u203e}{ED}$ is $ED=6$ meters
- The angle of the triangle is $\angle FED={30}^{\xb0}$.

Repeat same procedure to calculate the value of cosine at an angle ${30}^{\xb0}$ for the right angled triangle $FED$.

$cos{30}^{\xb0}=\frac{Length\; of\; the\; Adjacent\; side}{Length\; of\; the\; Hypotenuse}$

$\Rightarrow cos{30}^{\xb0}=\frac{EF}{ED}$

$\Rightarrow cos{30}^{\xb0}=\frac{5.196}{6}$

$\Rightarrow cos{30}^{\xb0}=0.866$

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