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Year 9 Maths Chapter 3 - Right-angled triangles

“the earth is flat” – our Year 9 maths teacher

You will want to refer to Year 8 Maths Chapter 6 for basic geometry. This section is more advanced, and omits basic concepts.

Table of Contents


a² + b² = c²

where a and b is the opposite/adjacent, and c is the hypotenuse

Pythagorean triads include 3, 4, 5 (because 3² + 4² = 5²) and 6, 8, 10 (because 6² + 8² = 10²).

Trig ratios

Take a right angled triangle with angle θ.

Trig ratios

  • The longest side of the triangle (opposite the right angle) is the hypotenuse.
  • The side opposite θ is the opposite.
  • The side adjacent to θ is the adjacent.

There are trig ratios for these sides: sine, cosine, and tangent, which are abbreviated to sin, cos and tan respectively.

In all of the below ratios, the side in the ratio refers to the length of a corresponding side. E.g opposite over adjacent = length of opposite side over length of adjacent side.

  1. Sine ratio
    sinθ = ––––––––––
  2. Cosine ratio
    cosθ = ––––––––––––
  3. Tangent ratio
    tanθ = ––––––––––

This can be remembered using the term:



Finding sides

More on Finding Sides at Khan Academy

  1. Find trig ratio
  2. With the trig ratio, replace θ with the (acute) angle stated
  3. Insert a pronumeral for the unknown side, into the trig ratio
  4. Solve

Finding sides

Finding angles

  1. Find trig ratio
  2. Insert the appropriate sides into their corresponding positions on the trig ratio
  3. Use sin⁻¹(your ratio here) to solve for the unknown angle

Finding angles

Angles of elevation and depression

More at Khan Academy on Angles of Elevation and Depression

  • The angle of elevation is how big the angle between a horizontal and a line of sight is. e.g when you look up, you are forming an angle of elevation
  • Similarly, the angle of depression is how big the angle between a horizontal and line of sight is, but instead of being up, it is down

Angle of elevation

Angle of elevation and depression

oof that meme


Measured clockwise from north


Chapter 3 Summary

Ch3 Summary

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