Mathematics Question and Solution
Calculating the required angle.
Let it be x.
Let 1 unit be the side length of the three congruent squares.
Let y be the side length of the green square.
a = 1+1
a = 2 units.
b = ½(y) units.
Calculating y.
2² = (½(y))²+y²
4 = ¼(y²)+y²
¼(5y²) = 4
y² = ⅕(16)
y = √(⅕(16))
y = ⅕(4√(5)) units.
y = 1.788854382 units.
Again, y is the side length of the green square.
Recall.
b = ½(y)
b = 0.5(1.788854382)
b = 0.894427191 units.
c²+b² = 1²
c² = 1-0.894427191²
c = 0.4472135955 units.
cosd = 0.894427191/1
d = acos(0.894427191)
d = 26.5650511771°
e² = 0.4472135955²+1²-2*0.4472135955*1cos26.5650511771
e = 0.63245553203 units.
(0.63245553203/sin26.5650511771) = (1/sinf)
f = 45°
g = 180-f
g = 135°
It implies, the required angle x is;
x = 360-90-g
x = 360-90-135
x = 135°
A smart approach is;
Considering angles on a straight line.
x = 180-½(90)
x = 180-45
x = 135°
