Tangent — Geometry, what it means and where it is taught
tan θ = oppositeadjacent.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Adjacent — The side next to that angle which is not the hypotenuse.
What uses it later
This idea is needed for:
- Arctangent — The inverse of tangent, restricted to outputs strictly between -90° and 90°.
- Derivative — The slope of the tangent, written f'(x) or dydx.
Practise this idea
4 questions in the course bank use Tangent, in Right Triangle Trigonometry, Rates of Change & the Derivative.
Problem 1
A ramp rises 1.5 m over a run of 9 m. Find the angle of elevation to one decimal place.
Worked answer
9.5
tan θ = 1.59 = 0.1667
θ ≈ 9.5°
Problem 2
From a point 30 m from a tower, the angle of elevation to the top is 52°. Find the tower height to the nearest metre.
Worked answer
38
tan 52° = h30
h = 30 × 1.2799 ≈ 38 m
Problem 3
For y=x2-8x+1, at what x is the tangent horizontal?
Worked answer
4
2x-8 = 0
x = 4
Problem 4
For y=x3-3x, find the positive x where the tangent is horizontal.
Worked answer
1
3x2-3 = 0
x2 = 1, so x = 1 or -1