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MArishka [77]
3 years ago
13

Please help I need to find the measure of the three unknown variables. Any help will be greatly appreciated:))

Mathematics
1 answer:
tiny-mole [99]3 years ago
7 0

Answer:

x = 8 \sqrt{3}

y = 60

z = 30

Step-by-step explanation:

To find x, use pythagorean theorem,

{x}^{2}  +  {8}^{2}  =  {16}^{2}

{x}^{2}  + 64 = 256

{x}^{2}  = 192

x=13.9 or 8 times sqr root 3( see later)

To find y, use cosine ratio.

\cos(y)  =  \frac{8}{16}

\cos(y)  =  \frac{1}{2}

y = 60

To find z, use triangle interior theorem

90 + 60 + z= 180

150 + z = 180

z = 30

Since this a 30-60-90 triangle, side x could be also written as

8 \sqrt{3}

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