Area 1/2=Absinc

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  • Topic: Triangle, Law of cosines, Area
  • Pages : 2 (303 words )
  • Download(s) : 161
  • Published : November 29, 2012
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Area 1/2=absinC

* (Obtuse Acute)

Area formula: Where b = base length and h = height.

When you have two sides and their included angle, the law of sine can be used in finding the area of the oblique triangle.

For the base, we use one of the sides - lets say we have base c For the height draw an perpendicular line from C to the base line c. * For the acute case an extended base line can be made to show this altitude, as h will touch the base outside the triangle. In the obtuse triangle do we now have two right triangles and find h by taking the sine:

Sin = opp/hyp

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Both is now sat equal to h and can be substituted in for the height in the originally triangle formula.

Eq. b sinA = h
Base: c

Area = (base)(height)
Area = (base)(b SinA)
Area= (c)(b SinA)

As it has no influence in which order the base and the opposite value comes, they will be arranged alphabetically.

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* Area = bc SinA

* When the base = c and the height = (a sin B):
When the base = c and the height = (b sin A):
 

 If eq. b were used as a base, the height would equal (a sin C):  

+ Example
+ label ABC

A= 65 degrees
b= 5
a= 7
c = 8

Area= .5 (b)(h)
To find the height take the Sin (opposite/hypp) then we’ll have h/b b= 5

Sin (A) = (h/b) = = bSin(A) = h
Sin(65) = (h/5) == 5Sin(65) = h

In order not to handle too many numbers we can substitute this into the area equation *
* Area = ½ (b)(h)
* Area = ½ (c)(bSinA) - Usually arranged alphabetically (bcSinA) *
* Then substitute the values into this new equation
*
* Area = 1/2 (8)(5Sin(65))
* Area = 16.53657358980207
* ≈ 16.54 cm2
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