Mathematics Question and Solution
Calculating Area BCA.
a = x+1+1+2+2
a = (6+x) units.
a is the height of the triangle.
b = x+1+1+2
b = (4+x) units.
c = (x+1) units.
Calculating x.
siny = 1/(x+1) --- (1).
siny = 2/(x+4) --- (2).
Equating (1) and (2).
1/(x+1) = 2/(x+4)
2(x+1) = x+4
2x+2 = x+4
2x-x = 4-2
x = 2 units.
Recall.
a = (6+x) units.
And x = 2 units.
a = 6+2
a = 8 units.
Again, a is the height of the triangle.
Recall Again.
c = (x+1) units.
And x = 2 units.
c = 2+1
c = 3 units.
sind = 1/3
d = asin(⅓)°
tand = e/a
tan(asin(⅓)) = e/8
e = 8tan(asin(⅓))
e = 2.82842712475 units.
e is half BC.
f = 2e
f = 2*2.82842712475
f = 5.65685424949 units.
f is BC, the base of triangle BCA.
It implies, area triangle BCA is;
½*a*f
= 0.5*8*5.65685424949
= 22.627416998 square units.
