Mathematics Question and Solution
Calculating length BP.
Let it be x.
a²+a² = 4²
2a² = 16
a² = 8
a = √(8)
a = 2√(2) cm.
a is AB, the side length of the square.
b = 45-30
b = 15°
b is angle CAP.
tan30 = c/(2√(2))
c = 2√(2)tan30
c = 1.63299316186 cm.
d = a-c
d = 2√(2)-1.63299316186
d = 1.19543396289 units.
e = (90-b)+45
e = 90-15+45
e = 120°
e is angle BCP.
f = e-90
f = 120-90
f = 30°
f is angle DCP
cos30 = g/d
g = 1.19543396289cos30
g = 1.03527618041 cm.
Therefore length BP, x is;
x² = 1.03527618041²+(2√(2))²-2*2√(2)*1.03527618041cos120
x = 3.46410161514 cm.
x = 2√(3) cm.
