Could someone please explain to me how I would find this out?
I have a triangle and I need to find the length of the line that would split it down the middle so that the areas were even.
A = 105 degrees
B = 42 degrees
C = 33 degrees
AB = 3.2
AC = 3.9
BC = 5.7
The line needs to be draw across the triangle splitting angle A (the 105 degrees angle).
The total area of the triangle is $6.075km^2$ , so the two halves have to be equal in area.
Can anyone help me out here? Thank you!
The line has to be drawn just through the midpoint of $BC$.
A median splits a triangle in two triangles having the same base and the same height, hence equal areas.
To find the length of a median you can use the formula: $$ m_a^2 = \frac{2b^2+2c^2-a^2}{4},$$ giving in your case: $$ m_a = \frac{1}{2}\sqrt{2\cdot 3.9^2+2\cdot 3.2^2-5.7^2}=2.145\ldots$$