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Update Unit 4: Trigonometry.md

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James Su 2019-11-26 13:51:47 +00:00
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Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md
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@ -62,7 +62,7 @@ If three sides of a triangle are respectively equal to the three sides of anothe
### Side-Angle-Side (SAS)
If two sides and the **contained** angle of a triangle are respectively equal to two sides and the **contained** angle of another triangle, then the triangles are congruent.
<img src="https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A77ca1d4d5a96259729f68cffe461702e9c92b5abb6018335683fa888%2BIMAGE_TINY%2BIMAGE_TINY.1" width="300">
<img src="https://sophialearning.s3.amazonaws.com/packet_logos/4004/large/Side%20Angle%20Side%20Triangle.gif?1308840229" width="300">
### Angle-Side-Angle (ASA)
If two angles and the **contained** side of a triangle are respectively equal to two angles and the **contained** side of another triangle, then the triangles are congruent.
@ -91,12 +91,12 @@ our big triangle's area is equal to $`\dfrac{k^2bh}{2}`$. Similar equations and
Three pairs of corresponding sides are in the **same ratio**
<img src="https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3Ac6e3b786fdc6105d64b086efcfa48c529b91cbb087f6ba3bc60b9f9f%2BIMAGE_TINY%2BIMAGE_TINY.1" width="500">
<img src="https://docs.google.com/drawings/d/snd5DSjJuOz9Lql5RgzUxCw/image?parent=1ltNI2q_ajTaJyAGt7C7GLY0uwh9LbBOfjW1B4Og_KwM&rev=59&h=188&w=398&ac=1" width="500">
### Side Angle Side similarity (RAR $`\sim`$)
Two pairs of corresponding sides are proportional and the **contained** angle are equal.
<img src="https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A3c5ec26759a40dc1d524b1c5af8864d5e87135063ce6f4e75d37af4d%2BIMAGE_TINY%2BIMAGE_TINY.1" width="500">
<img src="http://804369586450478528.weebly.com/uploads/4/5/2/6/45266747/775263614.png?367" width="400">
### Angle-Angle similarity (AA $`\sim`$)
Two pairs of corresponding angles are equal. In the diagram below, we can solve for the missing angle using Angle Sum Of A Triangle Theorem (ASTT) and see that those 2 triangle's angles are equal.
@ -166,7 +166,7 @@ In the ambigouous case, if $`\angle A, a, b`$ are given, the height of the trian
|Case|If $`\angle A`$ is **obtuse**|Condition|# & Type of triangles possible|
|:---|:----------------------------|:--------|:-----------------------------|
|5 |<img src="http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/image5.gif" width="200">|$`a \le b`$|no triangle exists|
|6 |<img src="http://www.gradeamathhelp.com/image-files/ambiguous-case-side-length.gif" width="200">|$`a \gt b`$|one triangle exists|
|6 |<img src="https://www.mathopenref.com/images/constructions/constaltitudeobtuse/step0.gif" width="300">|$`a \gt b`$|one triangle exists|
## Cosine Law