Valoarea unui unghi.
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- Mesaje: 244
- Membru din: Sâm Oct 30, 2010 3:55 pm
- Localitate: Bradenton, Florida
Valoarea unui unghi.
Fie un triunghi ABC şi un punct interior P astfel încât AB=5, AC=7, PB=2, PC=3 şi AP=BC. Să se determine valoarea unghiului <BPC (în grade).
- sunken rock
- Mesaje: 645
- Membru din: Joi Ian 06, 2011 2:49 pm
- Localitate: Constanta
Re: Valoarea unui unghi.
Drawing made to scale gives $\angle BPC=120^\circ$, also $\angle APB=\angle ABC$, but to solve ... Peru Geometrico.
Best regards,
sunken rock
Best regards,
sunken rock
A blind man sees the details better.
-
- Mesaje: 244
- Membru din: Sâm Oct 30, 2010 3:55 pm
- Localitate: Bradenton, Florida
Re: Valoarea unui unghi.
Multumesc. inca nu am reusit sa o rezolv. Am obosit gandindu-ma la ea. Weekend placut!
- sunken rock
- Mesaje: 645
- Membru din: Joi Ian 06, 2011 2:49 pm
- Localitate: Constanta
Re: Valoarea unui unghi.
Construction and "solution":
Take the equilateral triangle $BPD$ of side 2, extend (BD to A so that DA=3 and (DP to C so that PC=3. Clearly triangles ADP and CPB are congruent, so AP=BC; by cosine law calculate $AC: AC^2=25+9+15=49, AC=7$. By uniqueness of construction, we are done.
Best regards,
sunken rock
Take the equilateral triangle $BPD$ of side 2, extend (BD to A so that DA=3 and (DP to C so that PC=3. Clearly triangles ADP and CPB are congruent, so AP=BC; by cosine law calculate $AC: AC^2=25+9+15=49, AC=7$. By uniqueness of construction, we are done.
Best regards,
sunken rock
A blind man sees the details better.