$\Delta GHI$

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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