Answer:
X=[tex]8\sqrt{2}[/tex] Y=[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
The first one is 45-45-90 right angled isosceles triangle.
The length of the hypotenuse ie.X can be found with the help of Pythagoras Theorem.
[tex]a^{2} + b^{2} = X^{2}[/tex]
where a and b are the remaining sides of the triangle,
[tex]8^{2} +8^{2} =X^{2} \\2*8^{2} =X^{2}\\X=8\sqrt{2}[/tex]
X=[tex]8\sqrt{2}[/tex]
In the second triangle we have to apply trigonometry,
cos θ=[tex]\frac{Length OfAdjacentSide}{LengthOfHypotenuse}[/tex]
cos 30°=[tex]\frac{\sqrt{3} }{2}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex]=[tex]\frac{Y}{14}[/tex]
Thus, Y=[tex]7\sqrt{2}[/tex] inches
