Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
a² = 8²+12²-2*8*12cos60
a = 4√(7) cm.
b = 2a
b = 8√(7) cm.
(4√(7)/sin60) = (8/sinc)
c = 40.89339464928°
(16/sin40.89339464928) = (8√(7)/Sind)
d = 60°
e² = 12²+16²-2*12*16cos60
e = 4√(13) cm.
(a) Let beta be x. Calculating tanx.
(12/sinx) = (4√(13)/sin60)
x = asin(3√(39)/26)
It implies;
tanx is;
tan(asin(3√(39)/26))
= ⅕(3√(3))
(b) Calculating Orange hi Area.
f² = 6²+8²-2*6*8cos60
f = 2√(13) cm.
g² = 8²+24²-2*8*24cos60
g = 8√(7) cm.
(8/sini) = (8√(7)/sin60)
i =19.10660535063°
j = 40.89339464928-i
j = 21.78678929865°
k = 0.5(180-j)
k = 79.10660535068°
l = k-60
l = 19.10660535068°
(8/sinm) = (4√(13)/sin60)
m = 73.89788624801°
n = 180-m
n = 106.10211375199°
o = 6²+8²-2*8*6cos120
o = 2√(37)
(8/sinp) = (2√(37)/sin120)
p = 34.71500395395°
q = n - p
q = 71.38710979804°
r = 180-p-l
r = 126.17839069537°
s = 180-r
s = 53.82160930463°
t = 120-19.10660535068
t = 100.89339464932°
(u/sin100.89339464932) = (8/sin53.82160930463)
u = 9.73242004849 cm.
v = o-9.73242004849
v = ⅕(2√(37)) cm.
(w/sin71.38710979804) = (2√(37)/5sin(180-71.38710979804-53.82160930463)
w = 2.8221347318 cm.
Area Orange exactly in decimal is;
Area triangle with height ⅕(2√(37)) cm and base 2.8221347318sin53.82160930463
= 2.7712812921 cm²
(c) Calculating Length AG exactly.
Let it be y.
cos30 = 8/y
(√(3)/2) = (8/y)
y = ⅓(16√(3)) cm.
It implies;
(a) is ⅕(3√(3))
(b) is 2.7712812921 cm² exactly in decimal.
(c) is ⅓(16√(3)) cm.
