Mathematics Question and Solution
a² = 10²+5²
a = √(125)
a = 5√(5) units.
a = 11.1803398875 units.
a is the side length of the square.
tanb = 10/5
b = atan(2)°
c = atan(1/2)°
d = 45-c
d = (45-atan(1/2))°
d = 18.4349488229°
e = 45+d
e = 45+(45-atan(1/2))
e = 45+18.4349488229
e = 63.4349488229°
e = atan(2)°
sine = f/10
sin(atan(2)) = f/10
f = 8.94427191 units
cose = g/10
cos(atan(2)) = g/10
g = 4.472135955 units.
h = a-g
h = 5√(5)-4.472135955
h = 6.7082039325 units.
j = f-g
j = 8.94427191-4.472135955
j = 4.472135955 units
tank = h/f
k = atan(6.7082039325/8.94427191)
k = 36.8698976458°
l = 180-45-36.8698976458
l = 98.1301023542°
(4.472135955/sin98.1301023542) = (m/sin45)
m = 3.194382825 units.
Therefore, shaded area is;
Area triangle with height 8.94427191 units and base 6.7082039325 units - Area triangle with height 4.472135955 units and base 3.194382825sin36.8698976458 units.
= 0.5*8.94427191*6.7082039325-0.5*4.472135955*3.194382825
sin36.8698976458
= 30-4.2857142857
= 25.7142857143 square units.
Or
n = 180-45-(90-36.8698976458)
n = 81.8698976458°
(5√(5)/sin81.8698976458) = (o/sin45)
o = 7.9859570625 units.
Therefore, shaded area is;
0.5*7.9859570625*5√(5)sin(90-36.8698976458)-0.5*4.472135955²
= 35.7142857143-10
= 25.7142857143 square units.
