# Medians and sides

Triangle ABC in the plane Oxy; are the coordinates of the points:
A = 2.7
B = -4.3
C-6-1

Try calculate lengths of all medians and all sides.

Result

a =  10.77
b =  8.944
c =  7.211
t1 =  6.083
t2 =  8
t3 =  9.219

#### Solution:

$a=|BC| \ \\ a=\sqrt{ (-4-6)^2+(3-(-1))^2 }=2 \ \sqrt{ 29 } \doteq 10.7703 \doteq 10.77$
$b=|AC| \ \\ b=\sqrt{ (2-6)^2+(7-(-1))^2 }=4 \ \sqrt{ 5 } \doteq 8.9443 \doteq 8.944$
$c=|AB| \ \\ c=\sqrt{ (2-(-4))^2+(7-3)^2 }=2 \ \sqrt{ 13 } \doteq 7.2111 \doteq 7.211$

Try calculation via our triangle calculator.

$t_{1}=\sqrt{ 2 \cdot \ b^{ 2 }+2 \cdot \ c^{ 2 } - a^{ 2 } }/2=\sqrt{ 2 \cdot \ 8.9443^{ 2 }+2 \cdot \ 7.2111^{ 2 } - 10.7703^{ 2 } }/2 \doteq 6.0826 \doteq 6.083$
$t_{2}=\sqrt{ 2 \cdot \ c^{ 2 }+2 \cdot \ a^{ 2 } - b^{ 2 } }/2=\sqrt{ 2 \cdot \ 7.2111^{ 2 }+2 \cdot \ 10.7703^{ 2 } - 8.9443^{ 2 } }/2 \doteq 7.9998 \doteq 8$
$t_{3}=\sqrt{ 2 \cdot \ b^{ 2 }+2 \cdot \ a^{ 2 } - c^{ 2 } }/2=\sqrt{ 2 \cdot \ 8.9443^{ 2 }+2 \cdot \ 10.7703^{ 2 } - 7.2111^{ 2 } }/2 \doteq 9.2192 \doteq 9.219$

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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.

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