Mathematics Question and Solution
Let a be the radius of the circle.
2πa = 14π
a = 7 cm.
Calculating x.
cos49 = b/7
b = 7cos49
b = 4.59241320293 cm.
c = 2b
c = 9.18482640587 cm.
c is CD
d = 180-49-37.5
d = 93.5°
(9.18482640587/sin93.5) = (e/sin37.5)
e = 5.60181656513 cm.
Notice.
e = AB.
f = ½(AB)
f = 2.80090828257 cm.
Therefore, angle x is;
cosx = 2.80090828257/7
x = acos(2.80090828257/7)
x = 66.4137096823°
Calculating AD.
g = 49-37.5
g = 11.5°
h = 180-2(11.5)
h = 157°
j² = 7²+7²-2*7*7cos157
j = 13.7189458647 cm.
j is length AD.
Therefore;
Length AD - Length CD
= 13.7189458647-9.18482640587
= 4.53411945883 cm.
