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can anyone help find y? I tried looking it up but I couldn't find anything helpful.

image of y as altitude of right triangle

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    It seems to me that you should know [the altitude of a right triangle is the geometric mean](https://en.wikipedia.org/wiki/Geometric_mean_theorem) of the segments into which it divides the hypotenuse. – 2017-01-26

3 Answers 3

2

It is actually a trivial application of Geometric mean theorem

The proof is easy---- just use the knowledge of similar triangles!

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You have 3 similar triangles. That means that corresponding sides have the same ratios.

$\frac {\text{short leg}}{\text {log leg}} = \frac y{16} = \frac {4}{y}$

That is enough information to find $y.$

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In a right-angled triangle the hypotenuse is divided in two parts. Let´s call them $p$ and $q$. And the height of the triangle which belong to the hypotenuse is $h_c$. Then the formula is

$h_c^2=p\cdot q$

Taking the root

$h_c=\sqrt{p\cdot q}$

Whith the given values $h_c=\sqrt{4\cdot 16}=\sqrt{64}=8=y$