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36 votes
36 votes
"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 √(3)

x = 2 √(3)


"Solve for the variables x, y, and z in each triangle." I found some answers-example-1
User Ronak Mehta
by
3.2k points

1 Answer

17 votes
17 votes

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

User Lfjeff
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3.2k points