Mathematics Question and Solution
Let Alpha be x.
Calculating tanx.
Angle ABD = Angle ACD = y.
Let AB = AC = a.
Let AD = b.
b² = a²+10²-2a*10cosy
b² = a²+100-20acosy --- (1).
b² = a²+6²-2a*6cosy
b² = a²+36-12acosy --- (2).
cosy = a/10 --- (3).
Equating (1) and (2).
a²+100-20acosy = a²+36-12acosy
64 = 8acosy
8 = acosy
cosy = 8/a --- (4).
Substituting (3) in (4).
8/a = a/10
a² = 80
a = √(80)
a = 4√(5) units.
cosc = 4√(5)/10
c = acos(⅕(2√(5)))°
Calculating alpha (x).
180 = 2acos(⅕(2√(5)))+90+x
x = (90-2acos(⅕(2√(5))))
Therefore;
tanx is;
tan(90-2acos(⅕(2√(5)))) = ¾
tanx = ¾
