Finding x,
We will use Pythagoras theorem to determine the value of x:
[tex]9^{2} = {8}^{2} + {x}^{2} \\ 81 = 64 + {x}^{2} \\ 81 - 64 = {x}^{2} \\ {x}^{2} = 17 \\ x = \sqrt{17} [/tex]
Finding y,
We have to determine the angle, at the bottom left of the bigger triangle.
Using sine rule,
[tex] \frac{9}{sin(90)} = \frac{8}{sin(z)} \\ sin(z) = 0.8889 \\ z = {sin}^{ - 1} (0.8889) \\ z = 62.73[/tex]
To find the angle on the smaller triangle,
[tex]a = 90 - 62.73 \\ a = 27.27[/tex]
Finding the missing length of y,
[tex] \frac{ \sqrt{17} }{sin(62.73)} = \frac{m}{sin(27.27)} \\ m = 2[/tex]
So y = 2 + 8, y = 10
