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

Question

shadowfiend · Answer

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

anonymous · Answer

a triangle

anonymous · Answer

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

shadowfiend · Answer

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 · Answer

i dont know

shadowfiend · Answer

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

anonymous · Answer

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

shadowfiend · Answer

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 · Answer

about 28

shadowfiend · Answer

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

anonymous · Answer

so it cancels all the time?

shadowfiend · Answer

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 · Answer

y2 + 65 = 85

shadowfiend · Answer

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

anonymous · Answer

i mean 36

shadowfiend · Answer

Right :)

shadowfiend · Answer

Exactly.

anonymous · Answer

so now subtract 65 from both sides?

shadowfiend · Answer

Well, 36 :)

anonymous · Answer

yea

anonymous · Answer

y2=49

anonymous · Answer

$$\sqrt{49}$$

anonymous · Answer

7

shadowfiend · Answer

Pwned. Exactly.

anonymous · Answer

wow why cant my teacher explain this like this easy way

shadowfiend · Answer

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

anonymous · Answer

haha yea

anonymous · Answer

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 · Answer

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 · Answer

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

shadowfiend · Answer

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

anonymous · Answer

where do i find my other question?

anonymous · Answer

found it