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If triangle abc is not right, how to determine a side if given 2 sides and angle?work...

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mccee | Student, Undergraduate | (Level 1) eNoter

Posted August 21, 2012 at 4:06 PM via web

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If triangle abc is not right, how to determine a side if given 2 sides and angle?

work ab=2,ac=4,angle a=60

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted August 21, 2012 at 4:59 PM (Answer #1)

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Notice that the given angle `hatA`  is an included angle, hence, you may use the law of cosines to find the missing length such that:

`(BC)^2 = (AB)^2 + (AC)^2 - 2AB*AC*cos 60^o`

You need to substitute `2`  for `AB,4`  for `AC`   and `(1/2)`  for `cos 60^o` , such that:

`(BC)^2 = 2^2 + 4^2 - 2*2*4*(1/2)`

`(BC)^2 = 4 + 16 - 8 => (BC)^2 = 12 => BC = sqrt12 => BC = sqrt(2^2*3)`

`BC= 2sqrt 3`

Hence, evaluating the missing length, using the law of cosines, yields `BC= 2sqrt 3` .

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