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In △CDE , CD=12 , DE=5 , and m∠E=83∘ . What is m∠D to the nearest tenth of a degree? Enter your answer in the box.

 May 5, 2020
 #1
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                E  = 83

 

                   5 

 

C     12             D

 

We have the ambiguous case here

 

sin C / DE  = sin E /CD

 

sin C  / 5  = sin 83 / 12

 

sin C  =   5 * sin 83 / 12

 

arcsin   ( 5 sin 83 / 12)    = C   =  24.4°

 

So...in this  case    D  = 180  - 83  - 24.4   =   72.6°

 

The other possible value for C  = 180 - 24  =  156

 

But adding this to then known angle 83   is more than 180, so we only have one triangle

 

So   angle D  =  72.6°

 

 

cool cool cool

 May 5, 2020

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