Mathematics Question and Solution
Let a be the side of the inscribed square.
Calculating a.
tan60 = a/b
b = a/(tan60) cm.
Where b is BS = CR.
Therefore;
2b+a = 10
2a/(tan60)+a = 10
a((2/tan60)+1) = 10
a = 10(2√(3)-3) cm.
a = 4.64101615138 cm.
c = ½(10-a)
c = 0.5(10-4.64101615138)
c = 2.67949192431 cm.
Where c = b.
d = c+a
d = 2.67949192431+4.64101615138
d = 7.32050807569 cm.
Where d is BR.
e = atan(4.64101615138/7.32050807569)
e = 32.37365912705°
It implies;
Calculating TI, let it be f.
tan32.37365912705 = f/g
g = f/(tan32.37365912705)
Where g is BI.
tan45 = f/h
h = f/(tan45)
Where h is IR.
Therefore;
f/(tan32.37365912705) + f/(tan45) = 7.32050807569
f (1/(tan32.37365912705)+1/(tan45)) = 7.32050807569
f = 2.84032332089 cm.
Therefore;
TI = 2.84032332089 cm.
