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Question

# Suppose that a star forms an angle $\theta$ with respect to Earth and the sun. Let the coordinates of Earth be $(x, y)$, those of the star $(0,0)$, and those of the sun $(x, 0)$. Find an equation for $x$, the distance between the sun and the star, as follows.Solve your equation for $x$.

Solution

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We are tasked to give an equation that relates $x$ to the other given variables using trigonometric functions. The distance from the earth to the sun is $y$, $r$ is the earth's distance to the star, $x$ is the distance of the sun from the star, and $\theta$ is the angle between the earth and the sun. This implies that we are solving for the distance between the sun and the star.

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