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- anonymous

1. What is the value of h?
a. 4
b. 8 sqrt 3
c. 16
d. 8 sqrt 2

##### 1 Attachment

- whpalmer4

Okay, you have an isosceles right triangle here, because both of the angles are the same. What does that imply about the associated sides?

- anonymous

They have 2 equal sides and 2 equal angles?

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## More answers

- whpalmer4

Right. So what is the length of the other leg of the triangle?

- anonymous

4 ?

- whpalmer4

|dw:1393634970228:dw|
What is the value of ???

- anonymous

I'm still not sure .. /:

- whpalmer4

come on, we said this was an isosceles triangle, which means two equal angles and two equal sides!

- whpalmer4

Doesn't that mean ??? has to be 8?

- anonymous

why would it be 8 ?

- anonymous

sorry I feel stupid >_<

- whpalmer4

because it is an isosceles triangle. One of the sides is 8. Another one must be 8 as well, and it can't be the hypotenuse, because the hypotenuse is the longest side.

- whpalmer4

it's an isosceles triangle because it has two equal angles. You see that part, right?

- anonymous

ohhhhh ok I understand

- whpalmer4

So we can update our drawing: |dw:1393635393884:dw|
If the two sides labeled 8 are \(a=8,b=8\) respectively, what is the length of the hypotenuse, \(c\)? Use the Pythagorean theorem

- anonymous

k hold on

- anonymous

its a^2+b^2=c^2
do I add the 45 degrees together to get c? or is the 8?

- whpalmer4

The Pythagorean theorem relates only to the lengths of the sides. Angles don't matter (except, of course, that one of them must be 90 degrees for it to be a right triangle).

- whpalmer4

\[a^2+b^2=c^2\]\[8^2+8^2=c^2\]\[2*8^2 = c^2\]Take the square root of both sides:\[\sqrt{2*8^2} = \sqrt{c^2}\]Simplify\[8\sqrt{2} = c\]
If you have a \(45^\circ/45^\circ/90^\circ\) triangle such as this one, the side lengths are always in the ratio \(1:1:\sqrt{2}\)

- anonymous

is that the way you would do it for this kind of triangle too ?

##### 1 Attachment

- anonymous

@whpalmer4

- whpalmer4

I don't understand your question.

- anonymous

Use the Pythagorean theorem

- whpalmer4

Well, yes, if you know 2 sides in a right triangle, you can use the PT to find the 3rd side.

- anonymous

okay ty c:

- whpalmer4

you're welcome

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