# Distance findingDiscuss how trigonometry is used to find the distance from a point to a line .

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### 1 Answer

So, we have the equation of the line and a point, whose coordinates are known. The point is not on the given line.

We'll draw a parallel line to x axis, that is passing through the given point.

This parallel line is intercepting the given line into a point whose y coordinate is the same with the one of the given point. Since this intercepting point is on the given line, we'll find it's x coordinate substituting y coordinate into the equation of the line.

The distance from the given point to the given line is the perpendicular line to the given line.

We'll form a right angle triangle, whose hypotenuse is the line that is passing through the given point and the intercepting point.

The angle made by the given line to x axis represents the slope of the given line.

y = mx + n, where m is the slope.

to find the angle, we'll putĀ angle= arctan m

We could determine the distance, using sine function in the right angle triangle:

sine angle = distance/hypotenuse.