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Alty VonAltenstein
Republic Military School Minmatar Republic
0
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Posted - 2013.01.24 19:47:00 -
[1] - Quote
Suppose you have two triangles. The side and angles are unknown, but you do know the hypotenuse on both triangles are the same length and the shortest side on both triangles are also the same length. The third side is unknown. Would this mean the angle between the hypotenuse and the shortest side on both triangles are the same? |
Calico-Jack Daniels
344
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Posted - 2013.01.24 19:57:00 -
[2] - Quote
Alty VonAltenstein wrote:Suppose you have two triangles. The side and angles are unknown, but you do know the hypotenuse on both triangles are the same length and the shortest side on both triangles are also the same length. The third side is unknown. Would this mean the angle between the hypotenuse and the shortest side on both triangles are the same?
Triangle1: S^2 + L^2 = H^2
Triangle2: s^2 + l^2 = h^2
We know: s^2 = S^2 and h^2 = H^2
from this we get: L^2 = H^2 - S^2 for Triangle 1 and l^2 = h^2 - s^2 for triangle 2
knowing that both the hypotenuse AND the shortest side are equal on both triangles we can say that the hypotenuse minus the short side on both triangles is ALSO equal
So, our equation looks like this
L^2 = H^2 - S^2 = h^2 - s^2 = l^2
Therefore: L^2 = l^2 You have equal triangles and therefore the angle between the shortest side and the hypotenuse will be the same on both triangles. I go well with Quafe... |
Alty VonAltenstein
Republic Military School Minmatar Republic
0
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Posted - 2013.01.24 20:00:00 -
[3] - Quote
Also forgot to mention, we do know the angle between and the shortest side and the third side is the same on both triangles |
Calico-Jack Daniels
344
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Posted - 2013.01.24 20:03:00 -
[4] - Quote
Alty VonAltenstein wrote:Also forgot to mention, we do know the angle between and the shortest side and the third side is the same on both triangles
In case you want to "learn" something: Math Is Fun! I go well with Quafe... |
Akita T
Caldari Navy Volunteer Task Force
1624
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Posted - 2013.01.25 02:12:00 -
[5] - Quote
Alty VonAltenstein wrote:The side and angles are unknown, but you do know the hypotenuse on both triangles are the same length and the shortest side on both triangles are also the same length. ? When you used the word "hypotenuse", this means you have at least ONE angle known already, the right angle (the 90 degrees angle). You have one angle and two sides identical - the two triangles are identical. http://wiki.eveonline.com/en/wiki/User:Akita_T T2 BPO poll: https://forums.eveonline.com/default.aspx?g=posts&t=114789 Buying this: https://forums.eveonline.com/default.aspx?g=posts&t=147098 |
Caleidascope
Republic Military School Minmatar Republic
219
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Posted - 2013.01.25 03:25:00 -
[6] - Quote
Akita T wrote:Alty VonAltenstein wrote:The side and angles are unknown, but you do know the hypotenuse on both triangles are the same length and the shortest side on both triangles are also the same length. ? When you used the word "hypotenuse", this means you have at least ONE angle known already, the right angle (the 90 degrees angle). You have one angle and two sides identical - the two triangles are identical. I am with Akita T. Make sure those are right triangle. Since you say one side is hypotenuse, then we assume it is right triangle. Since it is right triangle, we can use the Pythagorean Theorem, that Calico-Jack Daniels explained, to fine the third side of both triangles. This will give you the proof that the two triangles are identical. You use the fact that two triangles are identical as proof that specific elements of each triangle are identical.
If I remember my geometry right, there are several ways to prove that two triangles are identical: 1) Show that two triangles have identical length sides. Say Triangle 1 has sides A, B, C. Triangle 2 has sides x, y, z. If you can show that A=x, B=y, C=z, then Triangle 1 = Triangle 2. Which in turn means that all the angles in Triangle 1 equal to corresponding angles in Triangle 2. 2) Show that all the angles in one triangle are equal to corresponding angles in second triangle. 3) Show that two sides and angle between them in one triangle are equal to corresponding two sides and angle in second triangle.
I have an ugly feeling that your triangles are not actually right triangles. In this case you can not use Pythagorean Theorem. However, there there are two laws that are very useful in this case, Law of Sines, Law of Cosines. Since you know two sides and one angle of each triangle, you can use the two laws to find all the missing pieces. The beauty of these laws is that they work on any triangle. Law of Sines: https://classroom.peoriaud.k12.az.us/sites/caylward/Classroom%20Images/Precal%20Sem%202/Trenton%20Flores/formula-picture-law-of-sines.gif Law of Cosines: http://www.mathwarehouse.com/trigonometry/images/law-of-cosines/law-of-cosines-formula-and-picture2.gif
P.S.: It sounds like you only need Law of Sines. Life is short and dinner time is chancy Eat dessert first! |
Brujo Loco
Brujeria Teologica
566
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Posted - 2013.01.25 17:30:00 -
[7] - Quote
Thought this was a post about Non Euclidean geometry pertaining the occult and the Hounds of TIndalos, left dissapointed Inner Sayings of BrujoLoco: http://eve-files.com/sig/brujoloco |
Caleidascope
Republic Military School Minmatar Republic
219
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Posted - 2013.01.26 01:45:00 -
[8] - Quote
Brujo Loco wrote:Thought this was a post about Non Euclidean geometry pertaining the occult and the Hounds of TIndalos, left dissapointed You know the matari dudes, we don't care about stupid wands, all we care is the triangulation of our UZIs.
Life is short and dinner time is chancy Eat dessert first! |
Surfin's PlunderBunny
Sebiestor Tribe Minmatar Republic
6979
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Posted - 2013.01.26 01:57:00 -
[9] - Quote
Why would I have 2 triangles? "Little ginger moron" ~David Hasselhoff-á |
Caleidascope
Republic Military School Minmatar Republic
220
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Posted - 2013.01.26 02:06:00 -
[10] - Quote
Surfin's PlunderBunny wrote:Why would I have 2 triangles? For engaging multiple targets. http://www.youtube.com/watch?v=uaJPd5qyW5I Life is short and dinner time is chancy Eat dessert first! |
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