Trigonometry: P,A,B,C points in plane s.t. <BPA, <CPA are obtuse and on opposite sides of PA

Stardust1

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Jun 14, 2023
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Hi, I was wondering how to solve this question. This is not straightforward and I am confused. The question is attached below
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Start with a sketch. Triangle ABC with point P inside of it. You can use law of cosines to find angle APB and angle APC, which would then lead to angle BPC. Now it's law of cosines to find BC. From there, you could use Hero's formula to find the area of the triangle.
 
Can you please elaborate for me? I've tried but I am getting nowhere close to the answer given.
 
Can you please elaborate for me? I've tried but I am getting nowhere close to the answer given.
Please SHOW what you tried, so we can see how far you really are from a reasonable solution:


At the very least, show us your sketch.
 
Did draw an approximate sketch?

If you did, please share a picture of the sketch - along with any mathematical work that you have done regarding this problem. Also let us know if you did not understand any "term" that you did not understand in responses 2 & 3.
 
Hi, I worked it out. It seems like I used the wrong formula and didn't do a step properly. Sorry about that.
 
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