Question

"Solve for the variables x, y, and z in each triangle."
I found some answers but I'm not entirely sure. Please help.
I got... but I'm not sure about x ...
$z = 10$
$y = 10 \sqrt{3}$
$x = 2 \sqrt{3}$
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Answer 1

Let O be the point on leg GK directly below the vertex at H.

Then triangles GOH and HOK are similar triangles, so that corresponding sides occur in a fixed ratio with one another. In particular,

GO/H.O = H.O/KO

5/x = x/15

x² = 75

x = √75

x = √(3 • 25)

x = 5√3

Solve for y and z using the Pythagorean theorem.

x² + 15² = y²

75 + 225 = y²

y = √300

y = √(3 • 100)

y = 10√3

x² + 5² = z²

75 + 25 = z²

z = √100

z = 10