find the value of y. express in simplest radical form.

- anonymous

find the value of y. express in simplest radical form.

- schrodinger

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- shadowfiend

This question doesn't make sense alone. Is there an equation involved?

- anonymous

a triangle

- anonymous

the hypotenuse is \[\sqrt{85}\] the base is y and the height is 6

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## More answers

- shadowfiend

Ok. So if it has a hypotenuse, then it is a right triangle. What equation did we say relates the sides of a right triangle?

- anonymous

i dont know

- shadowfiend

The Pythagorean theorem. Check the previous answer I gave you for what that looks like, and then let's continue.

- anonymous

ok but i never have done it with a radical of 85

- shadowfiend

Ok, so that's fine. Once we've said that \(a^2 + b^2 = c^2\), and we know that the hypotenuse is \(\sqrt{85}\), we have:
\[y^2 + 6^2 = \sqrt{85}^2\]
What's \(\sqrt{85}^2\)?

- anonymous

about 28

- shadowfiend

Not quite. The square root is the opposite of squaring something. So a square root and a square cancel out.

- anonymous

so it cancels all the time?

- shadowfiend

Right. So in \(\sqrt{x}^2 = x\). In this case, 85.
So we have:
\[y^2 + 6^2 = 85\]
Then you can solve for \(y\).

- anonymous

y2 + 65 = 85

- shadowfiend

\(6^2 = 6 \cdot 6\), which isn't quite 65.

- anonymous

i mean 36

- shadowfiend

Right :)

- shadowfiend

Exactly.

- anonymous

so now subtract 65 from both sides?

- shadowfiend

Well, 36 :)

- anonymous

yea

- anonymous

y2=49

- anonymous

\[\sqrt{49}\]

- anonymous

7

- shadowfiend

Pwned. Exactly.

- anonymous

wow why cant my teacher explain this like this easy way

- shadowfiend

That's a question I can't answer :)

- anonymous

haha yea

- anonymous

shadow what if the radical 19 is not the hypatenuse but its the height or base do i still keep 19 or do i do 19 x 19

- shadowfiend

When you plug into the quadratic equation, you'll still have it squared. So if it's \(\sqrt{19}\), then when you square it it will become 19.

- anonymous

ok thank you do you do trigonometry sin cos and tangent?

- shadowfiend

Sometimes. I saw your other question, but not sure what you're asking. Add some more details to it if you can.

- anonymous

where do i find my other question?

- anonymous

found it

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