Question

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

Answer 1

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

$8 \sqrt{3}$