Mathematics Question and Solution
a² = 2²+2²
Where;
a is radius of the ascribed half circle.
2 is the side length of the inscribed blue square.
a² = 8
a = 2√(2) cm.
Again, a is the radius of the circle.
Therefore, length AC is;
AC = a+2
AC = (2√(2)+2) cm.
AC = 2(√(2)+1) cm.
AC = 4.82842712475 cm.
tanb = 2/(2√(2))
b = atan(1/√(2))°
b = 35.2643896828°
c = 180-2b
c = (180-2atan(½√(2)))°
Therefore, length AP is;
(AP)² = 2(2√(2))²-2(2√(2))²cos(180-2atan(½√(2)))
AP = 4.61880215352 cm.
It implies;
AP ÷ AC is;
4.61880215352÷4.82842712475
= 0.95658524695
≈ 0.96 to 2 decimal places.
