The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.
<h3>What are the trigonometry ratios?</h3>
For a right angle triangle, the trigonometry ratios can be given as,
![\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}](https://tex.z-dn.net/?f=%5Crm%20%5Csin%20%5Ctheta%3D%5Cdfrac%7Bb%7D%7Bc%7D%5C%5C%5Crm%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7Ba%7D%7Bc%7D%5C%5C%5Crm%20%5Ctan%20%5Ctheta%3D%5Cdfrac%7Bb%7D%7Ba%7D)
Here, <em>a</em> is base side<em>, b</em> is perpendicular side and<em> c</em> is the hypotenuse side of the triangle.
In the given triangle, the length of base side<em> </em>is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.
![a=8\\b=6\\c=10](https://tex.z-dn.net/?f=a%3D8%5C%5Cb%3D6%5C%5Cc%3D10)
Thus, the tangent, cosine and sine ratios of angles X & Y are,
![\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Crm%20%5Csin%20%5Ctheta%3D%5Cdfrac%7B6%7D%7B10%7D%3D%5Cdfrac%7B3%7D%7B5%7D%5C%5C%5Crm%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B8%7D%7B10%7D%3D%5Cdfrac%7B4%7D%7B5%7D%5C%5C%5Crm%20%5Ctan%20%5Ctheta%3D%5Cdfrac%7B6%7D%7B8%7D%3D%5Cdfrac%7B3%7D%7B4%7D)
Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.
Learn more about the trigonometry angles here;
brainly.com/question/20519838
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