Adjacent — Geometry, what it means and where it is taught
The side next to that angle which is not the hypotenuse.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Hypotenuse — The side opposite the right angle — always the longest.
What uses it later
This idea is needed for:
Practise this idea
6 questions in the course bank use Adjacent, in Problem Solving, Right Triangle Trigonometry, Coordinate Geometry Proofs, Inverse Trigonometric Functions.
Problem 1
How many diagonals does a hexagon have?
Worked answer
9
Each vertex connects to 6 - 3 = 3 others by a diagonal
6 × 3 = 18, counting each diagonal twice
18 ÷ 2 = 9
Problem 2
Which ratio is oppositeadjacent?
Worked answer
tangent
tan θ = OA
Problem 3
tan θ = 1. Find θ.
Worked answer
45
θ = tan-1(1) = 45°
Problem 4
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 5
A(1,2), B(5,4), C(7,8), D(3,6). Is ABCD a rectangle? Answer yes or no.
Worked answer
no
Slope AB = 12, slope BC = 2
12 × 2 = 1, not -1
Not a right angle, so not a rectangle.
Problem 6
Find arctan 1 in degrees.
Worked answer
45
tan 45° = 1