Tangent ratio
I can derive the tangent ratio from the sides of a right-angled triangle.
Tangent ratio
I can derive the tangent ratio from the sides of a right-angled triangle.
Lesson details
Key learning points
- When the adjacent has a length of one, the opposite side has a length of tan(θ).
- You can apply a scale factor to this triangle to find the scaled length of the opposite side.
- There is a multiplicative link between two similar right-angled triangles.
- There is a multiplicative link within each right-angled triangle.
Common misconception
tan(60°) is double tan(30°).
The values of tan of an angle do not scale linearly. From the unit circle, we see that an angle of 30° meets a tangent to the circle at a height of approx. 0.58 units, whilst an angle of 60° meets the same tangent at a height of approx. 1.73 units.
Keywords
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Video
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Starter quiz
6 Questions
Exit quiz
6 Questions
sin(23°) -
0.39
cos(39°) -
0.777
tan(22°) -
0.404
tan(45°) -
1