Mathematics Question and Solution
Calculating Area Triangle APC, Area Yellow.
Let x be AP = CP
a = ½(10)
a = 5 cm.
a is the mid-point of AC.
Notice.
Since angle BAP = angle CAP is equal and length AP = length CP.
It implies;
AB = 5 cm.
cosb = (AB)/(AC)
cosb = 5/10
cosb = ½
b = acos(½)
b = 60°
b is angle BAC.
c = ½(b)
c = ½(60)
c = 30°
c is angle BAP.
Therefore;
Calculating x, AP = CP.
cosc = (AB)/x
cos30 = 5/x
½√(3) = 5/x
√(3)x = 10
x = 10/√(3)
x = ⅓(10√(3)) cm.
It implies, yellow area triangle APC is;
½*(AB)*(CP)
= ½*5*⅓(10√(3))
= ⅓(25√(3)) cm²
= 14.4337567297 cm²
