Mathematics Question and Solution
Observing the given yellow scalene triangle, an inscribed smaller scalene triangle that is similar the ascribed scalene triangle is identified.
Please, move the above question left/right one time to review the both similar scalene triangles.
Resolving the both triangles observing similar plane shape (scalene triangle) side length ratios.
It implies;
6 - 4
4 - b
Cross Multiply.
6b = 16
b = (8/3) units.
c = 6-b
c = (10/3) units.
It implies;
(10/3)² = (8/3)²+4²-2*4(8/3)cosd
(100/9) = (64/9)+16-(64/3)cosd
(64/3)cosd = (208/9)-(100/9)
(64/3)cosd = 12
cosd = 36/64
cosd = 9/16
d = acos(9/16)°
Therefore, the required length (?) is;
Let it be e.
e² = 6²+4²-2*4*6cos(acos(9/16))
e² = 52-(48*9)/16
e² = 52-27
e² = 25
e = 5 units.
Again, e is the required length.
