Mathematics Question and Solution
Calculating angle x.
a = 3-1
a = 2 units.
a is CD.
tanb = 3/1
b = atan(3)°
b is angle BCF equal angle ACD.
It implies;
((⅕(3√(10)))/sin(atan(3))) = (2/sinc)
c = asin(1)
c = 90°
c is angle CAD.
2² = d²+(⅕(3√(10)))²
d² = 4-⅕(18)
d = √(⅕(2)) I
d = ⅕√(10) units.
d = 0.63245553203 units.
d is AC.
e = 180-b
e = 180-atan(3)
e = 108.434948823°
e is angle ACB.
f² = 1²+0.63245553203²-2*1*0.63245553203cos(180-atan(3))
f = 1.3416407865 units.
f is AB.
Therefore;
Angle x ( angle BAC) is;
(1/sinx) = (1.3416407865/sin(180-atan(3)))
x = 45°
Area triangle ACB is;
½*⅕*√(10)*1sin(180+atan(3))
=⅒√(10)sin(180-atan(3))
= ⅒(3) square units.
= 0.3 square units.
