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;