Question

Solve simultaneously for the two equations for x and y


5x(cos 45) + 15y(cos 30) = 2,000

5x(sin45) - 15y(sin 30) = 0


I tried adding these two eqn. to elimate y and solve for x by adding [5 x cos 45] and [5 x sin 45] but the value for x is too high. Would I have to use trig identities to solve this equation for x and y?

Answer 1

Divide the first by 5, and replace the trig values
√2/2 x + 3√3/2 y = 400
times 2

√2x + 3√3y = 800

divide the 2nd by 5, and replace the trig values
√2/2 x - 3/2 y = 0
times 2
√2x - 3y = 0
√2x = 3y
sub that into the simplified first

3y + 3√3y = 800
y(3 + 3√3) = 800
y = 800/(3+3√3)
= 800/(3+3√3) * (3-3√3)/(3-3√3)
= 800(3)(1 - √3)/(9 - 27)

= (-400/3)(1 - √3) , after rationlizing

then
√2x = -400(1-√3)
times √2
2x = -400√2(1 - √3)

x = -200√2(1-√3)

approx. values:
x = 207.055
y = 97.607

Answer 2

Thank you very much, happy holidays