Dallasb22
What is the area of a right triangle with
Side a: 5√2
Side b: 4√2?
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Dallasb22
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Dallasb22
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I got 10..
Formula to find right angle:
A=1/2BH
muhammad9t5
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find the side and then use use heros formula.
muhammad9t5
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side c.
Dallasb22
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You mean to find C?
muhammad9t5
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yup
Dallasb22
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So i use: 5√2^2+4√^2=C^2
muhammad9t5
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by using pythagourus theorm
Dallasb22
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18=C^2
Dallasb22
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So i do √18
muhammad9t5
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thats 3redical2=c
muhammad9t5
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2sides are in radical then 3rd should be also in radical. do you know radical mean?
Dallasb22
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Yes the X√x right?
muhammad9t5
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yes great.
Dallasb22
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So it would be 9√2^2?
muhammad9t5
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\[18=\sqrt{3*3*2}\]
\[18=\sqrt{9*2}\]
u know the square roof of 9 is 3 then
\[18=3\sqrt{2}\]
Dallasb22
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Ok.
So C=3√2
Dallasb22
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What is the Hero's formula?
muhammad9t5
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therefor c=3redical2
Dallasb22
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A=5√2, B=4√2, C=3√2
muhammad9t5
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do you know about Hero's formula ?
CliffSedge
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If it's a right triangle, you don't need Heron's formula . . .
Dallasb22
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I don't know Heron's formula. And yes, it is a Right Triangle
CliffSedge
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Multiply a×b then divide by 2.
Dallasb22
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Nice of you to join us, Cliff
CliffSedge
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*salutes*
Heron's formula is general for any kind of triangle where you don't feel like using trigonometry to find the height. It requires that you know all three sides first, so often, you'll need trigonometry anyway.
Dallasb22
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5√2 * 4√2= 40
40/2= 20
CliffSedge
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QED. Good job.
muhammad9t5
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yes i am in that i am talking about Hero's formula not herons.
Dallasb22
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Okay, good to know, i googled Heron's formula. Hero formula=Heron's formula
CliffSedge
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Same guy. Heron is another name for Hero of Alexandria (en.wikipedia.org/wiki/Hero_of_Alexandria)
muhammad9t5
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ok me too.
Dallasb22
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I also, noted down Heron's formula for later use :D
So the area: 20?
Dallasb22
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Thanks Muhammad !
Dallasb22
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Thanks cliff!
Dallasb22
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I have another question if one of you don't mind
muhammad9t5
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its ok bro. u r welcome.
CliffSedge
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Heron's formula is pretty cool, but I prefer using the Law of Sines and Law of Cosines better (provided you know at least 1 angle.
muhammad9t5
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Step 2: Then calculate the Area using:
muhammad9t5
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means we were dong right or wrong?
muhammad9t5
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doing
muhammad9t5
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i was doing without angles.
CliffSedge
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Area of any triangle is half the product of the base and height. For a right triangle, the two perpendicular legs are the base and height.
muhammad9t5
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its easy for @Dallasb22
muhammad9t5
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ok lets see by using herons formula.
CliffSedge
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Actually, you were doing it with angles because you saw the right angle and used Pythagoras' theorem for the third side (which was unnecessary).
CliffSedge
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Be my guest. Heron's formula is a beast and not worth my time.
Dallasb22
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Yes, receiving the third side is only necessary if we use Heron's formula.
Dallasb22
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Correct?
CliffSedge
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and if it wasn't a right angle, then you'd have to use law of cosines or law of sines to find the third side, and if you're going to use trig anyway, might as well solve for the height instead (which is easier) and you still don't need Heron's formula.
Dallasb22
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@CliffSedge Another right triangle,
A=2√3 c=4
What do i do here?
Dallasb22
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Ah true, Cause 1/2BH=Area
Dallasb22
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I'd still only need base and height.
CliffSedge
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If you now have a leg and the hypotenuse, use PT to find the other leg then same as before.
CliffSedge
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As a fun exercise just to practice some arithmetic, you can use Heron's formula to verify the area, or vice-verse.
muhammad9t5
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what are the answers of 1st question?
Dallasb22
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Okay, so
2√3^2+b^2=4^2
6+B^2=16
Dallasb22
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@muhammad9t5 Answer for Q1 is 20
Dallasb22
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So i subtract 6 to both sides
B^2=10
Dallasb22
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B=√10
CliffSedge
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mm, something doesn't look right there..
Dallasb22
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They want my answer to be x√x
CliffSedge
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I think you forgot to square the 2 in (2√3)
Dallasb22
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Ahhhh. Thats my PROBLEM!!!
Dallasb22
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So it'd be 4√9 = 12
Dallasb22
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Side B= 2
Dallasb22
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So I would multiply A and B
2√3 * 2 =X
x/2=Area?
Dallasb22
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Giving me an area of: 4√3
CliffSedge
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did you divide by 2?
Dallasb22
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Ah man. *facepalm*
Dallasb22
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2√3 IS the area
CliffSedge
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Math teaches us to be precise and methodical, yes?
Dallasb22
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Hehe, yes it does.
Dallasb22
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I have 2 more if you don't mind.
Dallasb22
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They should be easy, they are equilateral.
Dallasb22
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I just am doing something wrong that I can't find..
CliffSedge
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And remember, that is more important than any particular kind of math problem. It's the problem-solving attitude, the patience, the planning, that is more important than whether or not you can solve this or that equation.
muhammad9t5
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yes.
CliffSedge
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Wanna take this equilateral triangle, muhammad? I'm going to take a coffee break.
Dallasb22
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Yes, i know what you mean.
If you didn't catch me I would have gotten it wrong, because I was rushing.
Dallasb22
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All three sides: 5, so the perimeter: 15
What is the area?
Dallasb22
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Equilateral triangle area formula: √3/4 * (s^2)
Dallasb22
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So √3/4 * (25)
Dallasb22
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I get: 25√3/4
Dallasb22
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|dw:1347039793370:dw|
Dallasb22
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But i cannot insert that in my work, i can only enter x√x
CliffSedge
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hmm, I'm getting something different. I'm going to doublecheck my work. In the meantime, if you forget the equilateral triangle formula, you can rederive it using (what else?) Pythagoras' theorem.
|dw:1347039924563:dw|
Dallasb22
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But what use is PT, if all side's are equal?
CliffSedge
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To solve for the height of the triangle, which you need for the general triangle area formula.
Dallasb22
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Okay.. So the height is 25?
25+25=25
50=25
25
Dallasb22
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Wait.. I did that wrong.
Dallasb22
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|dw:1347040273270:dw|
Dallasb22
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IF the sides are all 5, then AB is 2.5
Dallasb22
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So how do i put 2.5 into PT?
CliffSedge
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|dw:1347040269678:dw|
\[(S/2)^2+h^2=S^2 \rightarrow h^2=S^2-S^2/4 = 3S^2/4\]
CliffSedge
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Half of 5 is (5/2). (5/2)^2 = 25/4.
(tip: fractions are better than decimals when doing algebra)
CliffSedge
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I doublechecked. Your original formula and answer were correct.
Dallasb22
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How could that be?
CliffSedge
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How could what be?
Dallasb22
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25√3/4 is the answer?
CliffSedge
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Yep. If wherever you are submitting these answers doesn't like it in fraction form, then convert 25/4 into a decimal.
Dallasb22
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Being 6.25?
CliffSedge
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Yes. 2.5^2 = 6.25 just like 25^2 = 625.
Dallasb22
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But wait.. Something is wrong, because they want my answer as: x√x
CliffSedge
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And 6.25√3 is no good?
Dallasb22
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Darn, there i go again
I forgot we were only simplifying the 25/4
Dallasb22
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I kept including the 25√3
Dallasb22
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I included the radical in the the division...
Dallasb22
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So its 25/4√3
Or 6.25√3
Dallasb22
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Your Score: 100.0%
Thanks Cliff.
Dallasb22
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Those 2 were the only ones I was having trouble with.
CliffSedge
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My pleasure. They're all just puzzles. Keep looking until you find where all the pieces fit.
Dallasb22
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:)