Pythagorean Theorem and Triangles

Cake

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Hey Guys,

For number 31)

The answer is 4 sqroot 3.
I just want to know if I got the correct answer with the correct steps. I spent like 15 minutes with this question so I just want to be sure. I thought I knew how to get it. Turns out I don't. But anyways this is what I have tried.

So we have Right Triangle ABC.
Angle c = 90
Angle BAC = 30 because it has been bisected by Ray AD
AB = 12

Since we have 90 and 30 degrees. Angle B has to be 60 degrees.

AB = 12 so BD has to be the smallest number since it is opposite the 30 degree angle (applying 30-60-90 degree triangle)

So AB has to be the longest side since 4sqroot3 times sqroot 3 = 12.

The thing is how do I know AB is the longest side? It looks to me like it's the hypotenuse. Also, Angle DBC is not a right angle.

Brain is exploding. lol
 

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Hello :),

angle B has to be 30° because A= 60° and C= 90°.
Hypothenuse is always the longest side and opposite the right angle ;).
 
Hey Guys,

For number 31)

The answer is 4 sqroot 3.
I just want to know if I got the correct answer with the correct steps. I spent like 15 minutes with this question so I just want to be sure. I thought I knew how to get it. Turns out I don't. But anyways this is what I have tried.

So we have Right Triangle ABC.
Angle c = 90
Angle BAC = 30 because it has been bisected by Ray AD............ Incorrect angle BAC = 60 (given)
AB = 12

Since we have 90 and 30 degrees. Angle B has to be 60 degrees. ..........................Incorrect

AB = 12 so BD has to be the smallest number since it is opposite the 30 degree angle (applying 30-60-90 degree triangle)

So AB has to be the longest side since 4sqroot3 times sqroot 3 = 12.

The thing is how do I know AB is the longest side? It looks to me like it's the hypotenuse. Also, Angle DBC is not a right angle.

Brain is exploding. lol

Have you studied Law of Sines for triangles?

If you did → calculate angle BDA = ???

and apply Law of Sines.
 
Cricketeer Khan "s'got the angles" for you,
but if them Laws are Subhotoshic to you :rolleyes:
then you can solve this way:

"30-60-90" features means AC = 6, so
Big Pete Pythagoras says BC = 6SQRT(3)

Triangle ACD also being 30-60-90,
then CD = BD/2

Wrap it up...


I'm seriously lost. I understand 6SQRT(3) because one side is 6 and the other is 12. So CD is.. wait. I don't even know what BD is yet :(

Okay wait wait. I think I am close. So now that we know that AC = 6. We can find Triangle ADC. AD = 6SQRT(3). Then AD = 6SQRT(3) * 2 = 4 Radical 3. Then BD = CD*2 because the angle gets bisected, right?
 
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I'm seriously lost. I understand 6SQRT(3) because one angle is 6 and the other is 12.
Do you maybe mean that one "side" "has length" 6 and the other "side" "has length" 12? :shock:
 
Do you maybe mean that one "side" "has length" 6 and the other "side" "has length" 12? :shock:


Yeah, as you can tell, I am an expert on geometry. Lol. Is my reasoning correct though?
 
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