# Solving the Theta and Value of X (Sine Law)

I have this kind of equation that I produced using the Sine Law when I was answering a physics problem. How can I solve the value of $$\theta$$ and the value of $$x$$?

Sample Equation:

$$\frac{x}{\sin(44^\circ)} = \frac{250}{\sin(16^\circ + \theta)} = \frac{200}{\sin(120^\circ- \theta)}$$

• The last equality gives $\theta$. Hence you get $x$ from the first equality. Mar 5 '21 at 8:04
• Make orignal triangle with sides $x,200,250$ and angle $44,120-\theta,16+\theta$ respectively.Use cosine law on angle $44$ to find $x$.Once $x$ is find out You can find $\theta$ by taking $arcsin$ on both sides of equation $sin(16+\theta)=\frac{250 sin44}{x}$. Mar 5 '21 at 8:09
• @user10354138 Don't you think calculating $\theta$ from last inequality is much difficult. Mar 5 '21 at 8:27