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|dw:1435335512997:dw|

Do you know how to find the area of a triangle?

yes

bh/2

help someone...

|dw:1435338018836:dw|

|dw:1435338107837:dw|

Do you understand so far?

wait how do we know it's 60?

what about the triangle on the right side what do those angles equal to?

I'll show you each angle I found, one at a time, and will explain.

okay

okay

That makes angle ABC 90 degrees, and triangle ABC a right triangle.

|dw:1435338496200:dw|

right i remember all inscribed angles are 90 degrees

|dw:1435338551348:dw|

30 60 90 yea

Correct.

Now look at the congruent sides of triangle AOB.

|dw:1435338598897:dw|
Triangle AOB is isosceles. Opp angles to the congruent sides are congruent.

|dw:1435338640262:dw|

sorry i lost you

|dw:1435338690645:dw|

Triangle AOB is isosceles. Opp angles to the congruent sides are congruent.

what do u mean by that

Did you understand that angle A of triangle AOB is 60 deg?

yes

That means, in an isosceles triangle, the base angles are congruent.

hmmmm.... okay

|dw:1435338811305:dw|

yes angles B and C are equal

but the A is different....

so how does it relate

That means the base angles, BAO and ABO are congruent angles.

|dw:1435339099484:dw|

We now know that angle ABO also measures 60 deg.
|dw:1435339121331:dw|

Once two angles of a triangle are known, you can find the third angle.
60 + 60 + m

Now we know that triangle AOB is also equilateral in addition to being isosceles.

Cant it be this? |dw:1435339216515:dw|

then it wouldn't be 60 60 60

According to the given info, it must be equilateral.

okay thank you

im gonna have to look over this a few times im still having a hard time understanding why its all 60

This is not the end of the problem. We still need to find the area of triangle ABO.

|dw:1435339904347:dw|

Now the problem is simply to find the area of an equilateral triangle whose side has a length of 6.

so bh/2 right?

Yes, but we need to find the height.
Let's just look at the triangle now.

6 would be the opposite of 30 degrees

and height is given as \[6\sqrt{3}\]

|dw:1435339974085:dw|

ohhhhh yeaaaa

|dw:1435340010942:dw|

Inside triangle AOB, we have two 30-60-90 triangles.
|dw:1435340060713:dw|

so it would be \[9\sqrt{3}\]

Remember, the long leg is \(\sqrt 3\) times longer than the short leg.
|dw:1435340159438:dw|

|dw:1435340236323:dw|

i understand everything except how it's a 60-60-60- triangle

You are correct.

I'll show you that again, about the 60-60-60 triangle.

okay

yes

Ok?

yes yes

=)

Great.
Now let's concentrate only on triangle AOB.

|dw:1435340649665:dw|

so AO and BO makes it an isosceles

Yes, triangle AOB is isosceles.

|dw:1435340749447:dw|

but we dont now what AB is it could be anything

Yes, so far you are correct. We don;t know anything about AB.

|dw:1435340885281:dw|

i get it now ohhhhhhh okay wow i'm dumb that took me forever to get ...

\(\Huge \bf \color{red}{BINGO!!!} \)

Thank you so much <333333333333333333333333333333

You are very welcome.
I'm glad we took the extra time for you to understand it completely.

Couldn't have done it without you thanks!!!!!! =*)

You're welcome. Glad to help.