Mathematics Question and Solution
a = 180-75-35
a = 70°
(12/sin70) = (b/sin35)
b = 7.32464753257 cm.
c =2*35
c =70°
Calculating R, radius of the ascribed bigger circle.
d = ½(180-70)
d = 55°
R is;
(R/sin55) = (7.32464753257/sin70)
R = 6.38506663486 cm.
Calculating r, radius of the inscribed big circle.
(r/tan37.5) + (r/tan35) = 7.32464753257
r = 2.68167200695 cm.
(a) Radius Small ÷ Radius Large to 2 decimal places is;
2.68167200695 ÷ 6.38506663486
= 0.41999123272
≈ 0.42
(b) Calculating Area Orange in cm² to 1 decimal place.
(7.32464753257/sin70) = (e/sin35)
e = 4.4708717897 cm.
Area Orange is;
(0.5*12*7.32464753257sin75) - 2(0.5*4.4708717897*7.32464753257sin75)
= 42.45039732104 - 31.63171397403
= 10.81868334701
≈ 10.8 cm²
