Area of an Equilateral Triangle from an Interior Point

Problem

figure

Inside equilateral ABC\triangle ABC there is a point PP with PC>PBPC > PB. Given that BPC=150\angle BPC = 150^\circ, PA=5PA = 5, and SPBC=3S_{\triangle PBC} = 3, find SABCS_{\triangle ABC}.

Answer

Solution

Difficulty7/10
Topicsplane geometry, trigonometry, Law of Cosines, Triangle Geometry, Rotation

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments
Log in to join the discussion.

No comments yet.