Answer:y=9.01Step-by-step explanation:In this question you apply the Pythagoras Theorem to generate relationships which will enable you to form equations and solve for the unknown.The Pythagoras Theorem states that when you have a right-angle triangle and squares are made at each of the three sides, the sum of squares of the two small sides will equal the square of the longest side.It is expressed as a²+b²=c² where;a and b are the shortest sides of the triangle, where b is the heightc is the longest side of the triangle/hypotenuseIn the question we can use three triangles to form expressions using this theoremFirst triangleThat one with a height of y, short side of 3 and hypotenuse of zThe relationship you can form is; [tex]3^2+y^2=z^2\\9+y^2=z^2\\y^2=z^2-9------------------------(1)[/tex]In this equation you make y² the subject of the formulaSecond TriangleThe second triangle is that with a base of 27 as the (a), a height of y as the (b) and the hypotenuse of x as the (c)Hence the relationship you can form is[tex]27^2+y^2=x^2\\729+y^2=x^2\\y^2=x^2-729[/tex]In this equation you make y² the subject of the formulaThird TriangleThe third triangle is that one with a base of z as (a) , x as (b) which is the height and 30(3+27) as the (c) which is the hypotenuseThe relationship you can form is;[tex]z^2+x^2=30^2\\x^2=30^2-z^2---------------------(3)[/tex]Here x² is the subject of the formulaEquations[tex]y^2=z^2-9\\y^2=x^2-729\\x^2=900-z^2[/tex]Substitute equation 3 in equation 2[tex]y^2=x^2-729-------------2\\\\x^2=900-z^2-------------3\\\\y^2=900-z^2-729\\\\y^2=171-z^2---------------4[/tex]Substitute equation 4 in equation 1[tex]y^2=171-z^2---------------4\\\\y^2=z^2-9------------1\\\\z^2-9=171-z^2\\\\2z^2=171+9\\\\z^2=180\\\\z=\sqrt{180} \\\\z=9.487\\\\z=9.5[/tex]Use the value of z in equation 1 to get value of y[tex]z^2-3^2=y^2\\\\9.5^2-9=y^2\\\\90.25-9=y^2\\\\81.25=y^2\\\\\sqrt{81.25} =y\\\\y=9.01[/tex]