Mathematics Question and Solution
Calculating length CD.
Notice!
The composite plane shape is not drawn to scale.
tan60 = 8/a
a = 8/√(3)
a = ⅓(8√(3)) units.
a is OE.
(⅓(8√(3)))²+8² = b²
b² = ⅓(64)+64
b² = ⅓(64+192)
b² = ⅓(256)
b = ⅓(16√(3)) units.
b is CE.
Or
sin60 = 8/c
c = 8/sin60
c = 16/√(3)
c = ⅓(16√(3)) units.
c is CE.
(8/sin120) = (⅓(8√(3))/sind)
d = 30°
d is angle ODE.
It implies that DE = OE = ⅓(8√(3)) units.
Calculating CD.
Let it be e.
e² = (⅓(8√(3)))²+(⅓(16√(3)))²-2*⅓(8√(3))*⅓(16√(3))cos60
e² = ⅓(64)+⅓(256)-⅓(128)
e² = ⅓(320-128)
e² = ⅓(192)
e² = 64
e = √(64)
e = 8 units.
e is CD.
Or
f² = 8²+8²-2*8*8cos60
f = √(128-64)
f = √(64)
f = 8 units.
f is CD.
