please help. determine the value of cos(z). WX=6, XY=8, WY=10

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06-05-2022
Mathematics

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please help. determine the value of cos(z). WX=6, XY=8, WY=10

Sagot :

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Bhoopendrasisodiya34idn Bhoopendrasisodiya34idn · Answer 1 · 2022-05-09T07:39:45-04:00

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.

[tex]\tan \theta =\dfrac{b}{a}[/tex]

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,

[tex]\dfrac{YZ}{WY}=\dfrac{XY}{WX}\\\dfrac{YZ}{10}=\dfrac{8}{6}\\YZ=\dfrac{8}{6}\times10\\YZ=13.33[/tex]

By the right angle property,

[tex]\tan Z=\dfrac{WY}{YZ}\\Z=\tan^{-1}( \dfrac{10}{13.33})\\Z=36.9^o[/tex]

The value of cos(Z) is,

[tex]\cos Z=\cos 36.9\\\cos Z=0.8[/tex]

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.

Learn more about the right angle triangle property here;

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Sagot :

What is right angle triangle property?

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