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I have no idea what this means.

 

The diagram shows triangle KLM.  KL = 8.9 cm, LM = 8.8 cm, KM = 7.1 cm

 

N is the point on LM such that size of angle NKL = 3/5 * size of angle KLM.

 

Calculate the lengh of LN.

 

 Feb 21, 2021
 #1
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We  can manipulate the Law of Cosines  to  find  the  measure  of angle KLM

 

[7.1^2   -8.9^2  -8.8^2 ]  / [ -2 * 8.9 * 8.8]   =  cos  KLM

 

arccos   ( [7.1^2   -8.9^2  -8.8^2 ]  / [ -2 * 8.9 * 8.8] )  = KLM   ≈  47.29°

 

So  NKL  =  47.29  * 3/5    = 28.374°

 

So   angle KNL  = 180  -  47.29  - 28.374   = 104.336°

 

And  using  the Law of Sines

 

LN / sin NKL = KL /sin KNL

 

LN  / sin ( 28.374)  =  8.9 / sin ( 104.336)

 

LN  =   8.9 *sin (28.374)  / sin (104.336)  ≈  4.365

 

 

cool cool cool

 Feb 21, 2021

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