Question

I need to find tan (theta) for angle theta , the angle between the x-axis and the line that connects the origin to point (3,2)

Answer 1

tan(θ) = 2/3

Explanation:

You want the tangent of the angle θ between the x-axis and the line connecting the origin to point (3, 2).

Tangent

The tangent ratio is given by ...

Tan = Opposite/Adjacent

In the attachment, you can see that the side opposite the angle of interest is the y-coordinate of the point. The side adjacent is the x-coordinate. That means ...

tan(θ) = y/x

tan(θ) = 2/3

__

Additional comment

In general, the tangent of the angle a line makes with the x-axis is the slope of the line. Your line has slope 2/3, and that is the tangent of the angle it makes with the x-axis.