Mathematics Question and Solution
Let the adjacent base and adjacent height of the triangle be 3 units each.
a² = 2*3²
a = 3√(2) units.
b = ⅓(a)
b = ⅓(3√(2))
b = √(2) units.
c² = 2+9-6√(2)cos45
c = √(5) units.
(√(5)/sin45) = (√(2)/sind)
d = 26.56505117708°
e = 45-26.56505117708
e = 18.43494882292°
f = √(2)r units.
Calculating r.
r² =5+2r²-2√(5)*√(2)rcos18.43494882292
0 = r²+5-6r
r²-6r+5 = 0
Therefore;
Solving the quadratic equation.
r ≠ 5 units.
r = 1 unit.
Calculating the alpha, the required angle.
Let it be g.
sinh = 0.5√(2)/1
h = asin(½√(2))
h = 45°
It implies;
g (alpha) = 2h
g = 90°
