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anonymous
 one year ago
Please Help!!!!!
anonymous
 one year ago
Please Help!!!!!

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0O is the center of the semicircle. If angle BCO=30 degrees and BC = \[6\sqrt{3}\] what is the area of triangle ABO?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435335512997:dw

misssunshinexxoxo
 one year ago
Best ResponseYou've already chosen the best response.0Do you know how to find the area of a triangle?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338018836:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338107837:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you understand so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait how do we know it's 60?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what about the triangle on the right side what do those angles equal to?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1I'll show you each angle I found, one at a time, and will explain.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Start here. We have the side that is \(6 \sqrt 3\), the angle of 60 deg, and all three radii are congruent. dw:1435338257728:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now look at angle ABC. It is an inscribed angle. An inscribed angle is half the measure of the intercepted arc. Arc AC (on the bottom side) is 180 deg because it is a semicircle since we have the diameter AC.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That makes angle ABC 90 degrees, and triangle ABC a right triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338496200:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right i remember all inscribed angles are 90 degrees

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now look at triangle ABC. One angle is 90 deg. One angle is 30 deg. That means the left angle, angle A is 60 deg.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338551348:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now look at the congruent sides of triangle AOB.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338598897:dw Triangle AOB is isosceles. Opp angles to the congruent sides are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338640262:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Once you have two angles of triangle AOB are 60 deg each, the third angle must also be 60 deg, and it's an equilateral triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338690645:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Triangle AOB is isosceles. Opp angles to the congruent sides are congruent.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do u mean by that

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Did you understand that angle A of triangle AOB is 60 deg?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1There is a theorem that states: If a triangle has two congruent sides, then the angles opposite those sides are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That means, in an isosceles triangle, the base angles are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435338811305:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes angles B and C are equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but the A is different....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how does it relate

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. Now back to our problem. Notice that triangle AOB has two radii as sides, AO and OB. All radii in a circle are congruent, so sides AO and OB are congruent sides in a triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1That means the base angles, BAO and ABO are congruent angles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435339099484:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We now know that angle ABO also measures 60 deg. dw:1435339121331:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Once two angles of a triangle are known, you can find the third angle. 60 + 60 + m<AOB = 180 m<AOB = 60

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we know that triangle AOB is also equilateral in addition to being isosceles.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cant it be this? dw:1435339216515:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then it wouldn't be 60 60 60

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1According to the given info, it must be equilateral.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im gonna have to look over this a few times im still having a hard time understanding why its all 60

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1This is not the end of the problem. We still need to find the area of triangle ABO.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Triangle ABC is a 306090 triangle. AB is the short leg, and BC is the long leg. From the ratio of the lengths of the sides of a 306090 triangle, we have: \(1~:~ \sqrt 3~:~ 2\) for the ratio of short leg : long leg : hypotenuse

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We see that the long leg is \(\sqrt 3\) times the length of the short leg. That means the short leg is \(\sqrt 3\) times shorter than the long leg.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For triangle ABC, the short leg is AB, and the long leg is BC. Since AB is \(\sqrt 3\) times shorter than BC, AB is 6 units long.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435339904347:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now the problem is simply to find the area of an equilateral triangle whose side has a length of 6.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, but we need to find the height. Let's just look at the triangle now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.06 would be the opposite of 30 degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and height is given as \[6\sqrt{3}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435339974085:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435340010942:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Inside triangle AOB, we have two 306090 triangles. dw:1435340060713:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1XO is 3, since 3 is half of 6. Now we need h, the height of triangle AOB. h is also the long leg of the 306090 triangle BXO.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it would be \[9\sqrt{3}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Remember, the long leg is \(\sqrt 3\) times longer than the short leg. dw:1435340159438:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435340236323:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i understand everything except how it's a 606060 triangle

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we can find the area of triangle AOB: \(A = \dfrac{bh}{2} \) \(A = \dfrac{6 \times 3 \sqrt 3}{2} \) \(A = 9\sqrt 3\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are correct.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1I'll show you that again, about the 606060 triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You understood up to here that angle ABC is a right angle, and that angle BAC must be 60 deg.? dw:1435340411852:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now let's mark the congruent segments we have because they are radii of the circle. dw:1435340566038:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Great. Now let's concentrate only on triangle AOB.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435340649665:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so AO and BO makes it an isosceles

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We have a triangle, ABO, in the figure above. Sides AO and BO are congruent. That means the opposite angles, angles A and B are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, triangle AOB is isosceles.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435340749447:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but we dont now what AB is it could be anything

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes, so far you are correct. We don;t know anything about AB.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh noooooooooooooooooooooooo so because AO is 60 then BO would be 60 so the remaining would also be 60 .....

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We already know that angle A measures 60, so we can conclude that angle B also measures 60. That is because angles A and B are opposite congruent sides,so they must be congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435340885281:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i get it now ohhhhhhh okay wow i'm dumb that took me forever to get ...

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\Huge \bf \color{red}{BINGO!!!} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much <333333333333333333333333333333

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You are very welcome. I'm glad we took the extra time for you to understand it completely.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Couldn't have done it without you thanks!!!!!! =*)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You're welcome. Glad to help.
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