How can I solve simultaneous trigonometric equations involving cosine and sine?

[Joe_I_Am]

How would one go about solving the following equation?

242= 290cos(theta) + 187cos(phi)
0 = 290sin(theta) - 187sin(phi)


I have tried squaring both sides of both equations and adding them, and then using cos²x + sin²x = 1 to narrow some stuff down, and basically only found that:

phi + theta = 123.9 degrees.

But I still feel like I'm stuck. Maybe I'm missing an identity or something, I am terrible with those. Any help would be appreciated.

 

[Joe_I_Am]

Just realized I put this in the wrong forum,...sorry guys.

 

[Studiot]

Since this is homework, here are some strategy hints

Call your equations above 1,2,3

From 1 get cos$$\phi$$ in terms of cos$$\theta$$

From 2 get sin$$\phi$$ in terms of sin$$\theta$$

substitute into either the formula for

cos ($$\theta$$ + $$\phi$$)

or

sin ($$\theta$$ + $$\phi$$)

Substituting into 3 will get you an equation in a single unknown.