Part 1)
ok, so the cosine rule is a^2 = b^2 + c^2 - 2bcCos(A)
You're looking for angle so you rearrange the equation for that.
a^2 = b^2 + c^2 - 2bcCos(A)
2bcCos(A) = b^2 + c^2 - a^2
Cos(A) = (b^2 + c^2 - a^2)/2bc
A = Cos^-1((b^2 + c^2 - a^2)/2bc)
so if you sub in all the numbers...
A = Cos^-1((45^2 + 100^2 - 135^2)/2 x 100 x 45)
A = 133.5 degrees which = 134 degrees to 3 s.f.
Part 2)
ACB = 180 - ACD Due to angles on a line adding up to 180
As ACD = 123 degrees, ACB = 180 - 134 = 46 degrees
Part 3)
You use Sin(46) = x/100 ( sine of the angle = opposite / hypotenuse )
rearrange to find x
Sin(46) = x/100
multiply both sides by 100
100Sin(46) = x
x = 71.93 m
