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The value of cos(z), when the sides of the triangle are WX is 6, XY is 8 and WY is 10, is 0.8.

What is right angle triangle property?

In a right angle triangle, the ratio of the opposite side to the base side is equal the tangent angle made opposite to the opposite side.

$$\tan \theta =\dfrac{b}{a}$$

Here, (b) is the opposite side, (a) is the base side.

The two similar right angle triangle are shown in the image in which WX=6, XY=8, WY=10.

For the similar triangle, the ratio of two sides of a triangle is equal to the ratio of corresponding sides of the other triangle. Thus,

$$\dfrac{YZ}{WY}=\dfrac{XY}{WX}\\\dfrac{YZ}{10}=\dfrac{8}{6}\\YZ=\dfrac{8}{6}\times10\\YZ=13.33$$

By the right angle property,

$$\tan Z=\dfrac{WY}{YZ}\\Z=\tan^{-1}( \dfrac{10}{13.33})\\Z=36.9^o$$

The value of cos(Z) is,

$$\cos Z=\cos 36.9\\\cos Z=0.8$$

Thus, the value of cos(z), when the sides of the triangle are WX is 6, XY is 8 and WY is 10, is 0.8.

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