Question

The line to the right goes through the point (6, y). If the angle the graph makes with the x-axis is 22°, what is

the y-coordinate of the point to the nearest hundredth?

Answer 1

The y-coordinate of the point is approximately 2.42.

Explanation:

From the figure attached below the statement we derive the following equation to calculate the y-coordinate (
`y`), dimensionless, of the point in terms of the x-coordinate (
`x`), dimensionless, and angle of the line (
`\theta`), measured in sexagesimal degrees:

`y = x\cdot \tan \theta` (1)

If we know that
`x = 6` and
`\theta = 22^(\circ)`, then the y-coordinate of the point is:

`y = 6\cdot \tan 22^(\circ)`

`y\approx 2.42`

The y-coordinate of the point is approximately 2.42.