Mathematics Question and Solution
Calculating (ED)² +(DC)².
a² = √(3)²+√(3)²
a = √(6) units.
a is the radius of the ascribed half circle.
tanb = √(3)/a
b = atan(√(3)/√(6))
b = atan(1/√(2))
b = atan(½√(2))°
b = 35.2643896828°
b is angle OBG.
c = 180-2b
c = 180-2(35.2643896828)
c = 109.471220634°
c is angle BOC.
d = c-45
d = 109.471220634-45
d = 64.471220634°
d is angle COD.
e = 90+45-c
e = 135-109.471220634
e = 25.528779366°
e is angle DOE.
It implies;
(ED)² = 2√(6)²-2√(6)²cos25.528779366
(ED)² = 12-12cos25.528779366
(ED)² = 1.1715728753 square units.
(DC)² = 2√(6)²-2√(6)²cos64.471220634
(DC)² = 12-12cos64.471220634
(DC)² = 6.82842712465 square units.
Therefore;
(ED)²+(DC)² is;
1.1715728753+6.82842712465
= 8 square units.
