(a) Use the Law of Cosines to write an equation giving the relationship between x and θ
b=7in
a=1.5in
c=x
b^2=a^2+c^2-2ac*cos(θ)
7^2=1.5^2+x^2-2*1.5*x*cos(θ)
49=2.25+x^2-3x*cos(θ)
(b) Write x as a function of θ (Select the sign that yields positive values of x. )
49=2.25+x^2-3x*cos(θ)
0=2.25+x^2-3x*cos(θ)-49
x^2-3cos(θ)*x-46.75=0
x=(-(-3cos(θ)+-sqrt((-3cos(θ))^2-4*1*(-46.75))/(2*1)
select positive solution:
x=(3cos(θ)+sqrt(9cos^2(θ)+187)/2
