How do you solve for BOTH of the legs in a right triangle when only the hypotenuse is given?

Question

hero · Answer

Only if both legs of a right triangle are the same length is it possible to solve it.

parthkohli · Answer

But if you are given two angles...

parthkohli · Answer

You can use trig if one more angle is given to ye. :-)

hero · Answer

^Then we have a different situation

hero · Answer

I guess @leximakayla should just post her problem so we can help her better.

amistre64 · Answer

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if all you have is a hypot length, there are an infinite number of leg lengths that will satisfy it, but we can give a range or interval

hero · Answer

I guarantee you the user is NOT confused at this point.

anonymous · Answer

then the legs are the same length

parthkohli · Answer

Not really. The legs are of the same length if and only if we have two 45 degree angles.

anonymous · Answer

hold on ill post a pic

hero · Answer

Yes, I was just about to suggest that...again

anonymous · Answer

number 16

hero · Answer

:)

parthkohli · Answer

OK, that one is simply the Pythagorean Theorem.

parthkohli · Answer

Except the 16th.

hero · Answer

No, you can still use Pythagorean Theorem for the 16th

parthkohli · Answer

Actually, the 16th one too.

parthkohli · Answer

Yeah. :-P

anonymous · Answer

yes, but how do you use the pythagorean theorem when both legs are missing? thats the part i dont understand

parthkohli · Answer

Both legs are of the same length.

parthkohli · Answer

$$x^2 + x^2 = 6^2$$

hero · Answer

$$a^2 + b^2 = c^2$$

a = x = b
c = 6
$$x^2 + x^2 = 6^2$$
$$2x^2 = 36$$

Finish solving for x

anonymous · Answer

$$x = \sqrt{18}$$

hero · Answer

Which equals $$\sqrt{9 \times 2}$$ which equals
$$\sqrt{9} \times \sqrt{2}$$

Which equals...?

anonymous · Answer

$$3\sqrt{2?}$$

hero · Answer

Well, without the question mark under the radical :P

anonymous · Answer

i didnt mean to put that :)