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

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

a triangle

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

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?

i dont know

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

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

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 \(\sqrt{85}^2\)?

about 28

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

so it cancels all the time?

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

y2 + 65 = 85

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

i mean 36

Right :)

Exactly.

so now subtract 65 from both sides?

Well, 36 :)

yea

y2=49

\[\sqrt{49}\]

7

Pwned. Exactly.

wow why cant my teacher explain this like this easy way

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

haha yea

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

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.

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

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

where do i find my other question?

found it

Join our real-time social learning platform and learn together with your friends!