Mathematics Question and Solution
Calculating Length x.
a² = 2²+(2+1)²
a = √(13) units.
a is the each of the two adjacent lengths of the green isosceles right-angled triangle.
tanb = 3/2
b = atan(3/2)°
c = 45-atan(2/3)
c = 11.309932474°
2√(13)² = d²
d = √(26) units.
e² = √(26)²+2²-2*2√(26)cos11.309932474
e = 3.16227766017 units.
f = 90-atan(3/2)
f = 33.690067526°
g² = 1+√(13)²-2√(13)cos33.690067526
g = 2.82842712475 units.
h² = 2(1)²
h = √(2) units.
2.82842712475² = √(2)²+3.16227766017²-2*3.16227766017√(2)cosj
8.94427191cosj = 4
j = acos(0.4472135955)
j = 63.4349488229°
Therefore, calculating x.
sinj = x/√(2)
x = √(2)sin(63.4349488229)
x = 1.26491106407 units.
