Grade 10

Trigonometry Intro

Learn how angles and sides of right-angled triangles are connected — and how to use that to solve real-world problems.

Right-angled triangles

A right-angled triangle has one angle of exactly 90°. The sides have special names depending on which angle you are focusing on:

θadjacentoppositehypotenuse
Theorem
  • Hypotenuse — the longest side, always opposite the right angle
  • Opposite — the side directly across from angle θ
  • Adjacent — the side next to angle θ (not the hypotenuse)
The hypotenuse is always the same side. But "opposite" and "adjacent" change depending on which angle you choose as θ.
Theorem
hyp2=opp2+adj2\text{hyp}^2 = \text{opp}^2 + \text{adj}^2

Use this when you know two sides and need the third, without using trigonometry.

Worked Example

A right triangle has legs of 6 and 8. Find the hypotenuse.