Section 14 - 4: Area and The Law of Sines
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Mathematics
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10th - 12th Grade
•
Medium
Standards-aligned
Abbie Gutzmer
Used 17+ times
FREE Resource
7 Slides • 9 Questions
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Section 14 - 4: Area and The Law of Sines
To find different unknowns in oblique triangles.
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Formula for AREA of Oblique Triangle
Area = (a*c*sinB)/2 or (b*c*sinA)/2 or (a*b*sinC)/2
Why it works...
Area = (h*a)/2
sinB=h/c so h = c*sinB replace h in area formula.
sinC = h/b so h = b*sinC replace h in area formula.
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An example
Formula for area: (side 1)(side 2)(sin(included angle))/2
(12*(8.2)*sin114)/2
=44.95 square units
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Multiple Choice
Find the Area of the Triangle.
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Multiple Choice
Find the Area of the Triangle.
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Multiple Choice
Find the Area of the Triangle.
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Law of Sines
Let's look at that same triangle and think about the height.
sinB=h/c so h = c*sinB replace h in area formula.
sinC = h/b so h = b*sinC replace h in area formula.
If they both equal "h" then they must equal each other.
c*sinB=b*sinC
SO...b/sinB = c/sinC
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Multiple Choice
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Multiple Choice
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Please change 19 m for side BC to 21 meters! Thanks!
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Multiple Choice
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Multiple Choice
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Multiple Choice
Find the area of ABC to the nearest tenth.
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Multiple Choice
Find m<B
Section 14 - 4: Area and The Law of Sines
To find different unknowns in oblique triangles.
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