Mathematics Question and Solution
Let a be the radius of the quarter circle.
b = x°
c = (45-x)°
It implies;
sinx = 1/a --- (1).
sin(45-x) = 2/a --- (2).
At (1).
a = 1/sinx --- (3).
Substituting (3) in (2).
sin(45-x) = 2/(1/sinx)
sin(45-x) = 2sinx
sin45cosx-cos45sinx = 2sinx
½√(2)(cosx-sinx) = 2sinx
cosx-sinx = 2√(2)sinx
cosx = 2√(2)sinx+sinx
cosx = (2√(2)+1)sinx
cosx/sinx = (2√(2)+1)
sinx/cosx = 1/(2√(2)+1)
tanx = (2√(2)-1)/7
x = atan((2√(2)-1)/7)
x = 14.6388065952°
Calculating a, radius of the quarter circle.
Recall.
At (1).
sinx = 1/c, and x = 14.6388065952°
Therefore;
sin14.6388065952 = 1/a
a = 1/sin14.6388065952
a = 3.956874303 units.
Or
At (2).
sin(45-x) = 2/a
And x = 14.6388065952°
Therefore;
sin(45-14.6388065952) = 2/a
sin30.3611934048 = 2/a
a = 2/sin30.3611934048
a = 3.956874303 units.
Again, a is the radius of the quarter circle.
