6 review questions help please? medal!

Question

anonymous · Answer

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

whpalmer4 · Answer

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 · Answer

They have 2 equal sides and 2 equal angles?

whpalmer4 · Answer

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

anonymous · Answer

4 ?

whpalmer4 · Answer

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

anonymous · Answer

I'm still not sure .. /:

whpalmer4 · Answer

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

whpalmer4 · Answer

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

anonymous · Answer

why would it be 8 ?

anonymous · Answer

sorry I feel stupid >_<

whpalmer4 · Answer

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 · Answer

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

anonymous · Answer

ohhhhh ok I understand

whpalmer4 · Answer

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 · Answer

k hold on

anonymous · Answer

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

whpalmer4 · Answer

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 · Answer

$$a^2+b^2=c^2$$$$8^2+8^2=c^2$$$$2*8^2 = c^2$$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 · Answer

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

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

I don't understand your question.

anonymous · Answer

Use the Pythagorean theorem

whpalmer4 · Answer

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

anonymous · Answer

okay ty c:

whpalmer4 · Answer

you're welcome