Mathematics Question and Solution
a = 180-20-50-40
a = 70°
It implies the triangle is isosceles.
Let the base of the isosceles triangle be 1 unit.
1² = 2b²-2b²cos40
1 = 0.4679111138b²
b = √(1/0.4679111138)
b = 1.4619022 units.
b is the two equal lengths of the isosceles triangle.
c = 180-40-20
c = 120°
(1.4619022/sin120)
= (d/sin20)
d = 0.5773502692 units.
(1.4619022/sin120)
= (e/sin40)
e = 1.0850635751 units.
f = e-d
f = 1.0850635751-0.5773502692
f = 0.5077133059 units.
g = b-d
g = 1.4619022-0.5773502692
g = 0.8845519308 units.
h² = 0.5077133059²+1-2*0.5077133059*1cos50
h = 0.7778619134 units.
j = 180+120
j = 60°
Therefore the required angle alpha is;
Let it be k.
(0.8845519308/sink) = (0.7778619134/sin60)
k = 80°
Again, k is alpha, the required angle.
