Answer:
[tex]x = 8 \sqrt{3} [/tex]
[tex]y = 60[/tex]
[tex]z = 30[/tex]
Step-by-step explanation:
To find x, use pythagorean theorem,
[tex] {x}^{2} + {8}^{2} = {16}^{2} [/tex]
[tex] {x}^{2} + 64 = 256[/tex]
[tex] {x}^{2} = 192[/tex]
x=13.9 or 8 times sqr root 3( see later)
To find y, use cosine ratio.
[tex] \cos(y) = \frac{8}{16} [/tex]
[tex] \cos(y) = \frac{1}{2} [/tex]
[tex]y = 60[/tex]
To find z, use triangle interior theorem
[tex]90 + 60 + z= 180[/tex]
[tex]150 + z = 180[/tex]
[tex]z = 30[/tex]
Since this a 30-60-90 triangle, side x could be also written as
[tex]8 \sqrt{3} [/tex]
