1. 15G – 15J Sine and Cosine Rules
Unit 6: Geometry and Trigonometry
15G, 15H, 15I, 15J
5/8/ :26 AM

2. Terminology
oblique triangles: non-right triangles (acute or obtuse) triangle congruence method: usually used to prove two triangles have the same shape and size; can also be used to show that when you construct a triangle with three given measures, you can only construct one unique shape Methods SSS SAS ASA AAS “Non-Methods” SSA AAA SAS SSS SSA/SAS (mismatched)
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15G, 15H, 15I, 15J
5/8/ :26 AM

3. Congruence Methods
SSS AAS SAS
15G, 15H, 15I, 15J
5/8/ :26 AM

4. Oblique Triangle Rules
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sides a, b, and c are across from angles A, B, and C respectively
Sine Rule
AAS, ASA, SSA
SSA: none, one, or two unique triangles with the given measures
if the side length opposite the given angle is less than the other length, construct an isosceles triangle and check for the “ambiguous case” (second triangle) by comparing angles
15G, 15H, 15I, 15J
5/8/ :26 AM

5. SSA and the Ambiguous Case
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A = 60°, a = 10, b = 16
not possible to construct
(not particular to SSA)
A = 25°, a = 7, b = 11
two triangles
15G, 15H, 15I, 15J
5/8/ :26 AM

6. Oblique Triangle Rules
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Cosine Rule
SAS, SSS
SAS: find remaining side first and then… (see SSS)
SSS: use the cosine rule to find the largest angle; use either rule past that point
The sine and cosine rules work for right triangles but they are less efficient than using right triangle trigonometry (SOH CAH TOA).
15G, 15H, 15I, 15J
5/8/ :26 AM

7. Finding the Largest Angle
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A = 33°, b = 9, c = 13
Find the remaining side.
Why is C the largest angle?
How does using the sine rule instead of the cosine rule impact calculating C?
15G, 15H, 15I, 15J
5/8/ :26 AM

8. Domain and Range
What impact does the range of the inverse trig functions have on finding angles in:
right triangle trigonometry? SOH CAH TOA
“oblique triangle” trigonometry? Sine Rule, Cosine Rule
Therefore if you have an oblique triangle and you know all three side lengths, USE THE COSINE RULE TO FIND THE LARGEST ANGLE (across from the longest side).
If the angle is obtuse, you’ve avoided the only potential issue. If it’s acute, there are no obtuse angles. After you have the largest angle measure, you can then use either rule.
15G, 15H, 15I, 15J
5/8/ :26 AM