Mathematics Question and Solution
Calculating r, radius of the inscribed circle.
Notice.
Angle ABD = ¼(60)
Angle ABD = 15°
tan30 = r/a
1/√(3) = r/a
a = √(3)r units.
b = 2a
b = 2√(3)r units.
b is the side length of the ascribed regular triangle.
(1/sin15) = (√(7)/sinc)
c = 43.2175867282°
c is angle DAB.
d = 180-15-43.217586782
d = 121.782413272°
d is angle ADB.
Calculating r.
((2√(3)r)/sin121.782413272) = (1/sin15)
r = (sin121.782413272)/(2√(3)sin15)
r = 0.94811248631 units.
