Mathematics Question and Solution
Notice.
4 units is the radius of the inscribed circle.
a² = 2(4)²
a = 4√(2) units.
8² = (4√(2))²+4²-2*4*4√(2)cosb
64 = 32+16-32√(2)cosb
32√(2)cosb = 48-64
cosb = -16/(32√(2))
b = acos(-1/(2√(2)))
b = acos(-¼√(2))
b = 110.704811055°
c = 180-b
c = 69.2951889454°
Calculating x.
Let x = 2d.
And;
sin69.2951889454 = d/4
d = 4sin69.2951889454
d = 3.74165738677 units.
Therefore;
x = 2*3.74165738677
x = 7.48331477355 units.
