Triangle's centroid

In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°.
Calculate the length of the BC side to 2 decimal places.

Correct answer:

a =  10.58 cm

Step-by-step explanation:

tc=9 cm ta=6 cm CTS=60 rad=60 π180 =60 3.1415926180 =1.0472=π/3  CT=21+2 tc=21+2 9=6 cm ST=11+2 ta=11+2 6=2 cm  x2=CT2+ST22 CT ST cosCTS  x=CT2+ST22 CT ST cos(CTS)=62+222 6 2 cos(1.0472)=2 7 cm5.2915 cm  a=2 x=2 5.2915=4 7=10.58 cm



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