https://youtu.be/O8M4ZErxE-M

In this video I go over quick derivation of a formula for the angle between two intersecting lines, and derive it such that it is in terms of the slopes of the lines. The interesting part of this formula is that it mirrors the tan(x – y) trigonometric identity formula which I solved in my last video. The derivation involves first writing the angle between the two lines in terms of the angles of the two line that are made from the horizontal axis. From here we can apply the tan(x – y) trigonometric identity and realize that the tangent terms are equivalent to the two slopes! This is a very interesting formula about the angle between two lines, and I will be using it in my later videos so make sure to watch this video!

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# Formula of Angle Between Two Lines Using Their Slopes


![Angle Between Two Lines.jpeg](https://files.peakd.com/file/peakd-hive/mes/23tHdQDGmr8TzjnGeomNkm7yYA4kFijc5hXT9B2KGZgUfWqsA4T6UY9qbbxFdF8rjjtap.jpeg)


Use the identity for tan(x - y) to show that if two lines L<sub>1</sub> and L<sub>2</sub> intersect at an angle α, then:

![](https://steemitimages.com/DQmY3WpRpYmxkmHNngivtnEghyvVfq2Af661S25Rx7PwMGm/image.png)

Where m<sub>1</sub> and m<sub>2</sub> are the slopes of L<sub>1</sub> and L<sub>2</sub>, respectively.

![](https://steemitimages.com/DQmWK1mazHnfCj17visXZ9srGUcykqZceueXJTcTXBwaKzQ/image.png)

![](https://steemitimages.com/DQmctEeLWRvHhNzEtp36pBp4MnGYM1ezJ4yc8NJuyDWvzt8/image.png)

![](https://steemitimages.com/DQmbrhDR1YxKJP9a1xHgQRi2hxvGF8AsJJMXbhWuwZUPnQp/image.png)