Success TutoringWorksheets
Download Free PDF
Cheat SheetYear 9Level 2 · Standard

Free Year 9 Trigonometry Cheat Sheet: SOH CAH TOA

A compact reference for right-angled triangle trigonometry in Year 9: labelling the opposite, adjacent and hypotenuse, choosing sine, cosine or tangent, finding an unknown side (whether it is on the top or the bottom of the ratio) and finding an unknown angle with the inverse functions. Includes a ladder problem and calculator-mode warnings.

Download Free PDF

Instant download · No sign-up · Free for personal, classroom and homeschool use

Year
Year 9
Subject
Mathematics
Topic
Trigonometry
Difficulty
Level 2 · Standard
Estimated time
20 minutes
Curriculum
Australian Curriculum
Answers
Not applicable
Format
PDF (A4) + print

Students will practise

  • understanding how to label the hypotenuse, opposite and adjacent sides relative to an angle
  • choosing the correct trigonometric ratio from the sides involved
  • finding an unknown side length in a right-angled triangle
  • finding an unknown angle using inverse sine, cosine and tangent

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Trigonometry Cheat Sheet: SOH CAH TOA

  1. 1Year 9 Trigonometry (Finding Sides) Worksheet — Level 1
Study guide

How to use this cheat sheet

  1. Read it together first, pausing at each worked example to try the step before reading the answer.
  2. Attempt the "Check yourself" questions at the end without looking back.
  3. Then practise with a worksheet from the pathway above and finish with the topic test.

Common questions

Who is this cheat sheet for?

Year 9 students (typically ages 14–15) working on trigonometry. It is pitched at level 2 · standard.

Are the answers included?

This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.

How long does it take?

About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try Year 9 Trigonometry (Finding Sides) Worksheet — Level 1.

Preview

Year 9 · Mathematics · Trigonometry

Trigonometry Cheat Sheet: SOH CAH TOA

Success Tutoring

Student name:

Date:

What you need to know

Trigonometry links the angles of a right-angled triangle to the ratios of its sides. First, label the three sides relative to the angle you are working with (call it θ, theta): the hypotenuse is the longest side, opposite the right angle; the opposite side is across from θ; the adjacent side is next to θ but is not the hypotenuse. If you switch to the other acute angle, opposite and adjacent swap.

The memory aid is SOH CAH TOA: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent.

RatioFormulaUse it when the question involves
sinesin θ = the opposite side and the hypotenuse
cosinecos θ = the adjacent side and the hypotenuse
tangenttan θ = the opposite side and the adjacent side

Method for every question. 1. Label the sides from the angle. 2. Cross out the side you do not know and do not want; the two left tell you which ratio to use. 3. Write the equation. 4. Rearrange and solve, making sure your calculator is in degrees mode. 5. Round only at the end and check the answer is sensible (the hypotenuse must be the longest side).

Find x, the side opposite a 35° angle, when the hypotenuse is 12 cm

  1. Sides involved: opposite (x) and hypotenuse (12). Use sine.
  2. sin 35° = .
  3. x = 12 × sin 35° = 12 × 0.5736… = 6.88 cm (to 2 decimal places).
  4. Sensible? 6.88 is shorter than the hypotenuse 12, and the angle is less than 45°, so the opposite side should be less than half-ish of the hypotenuse. Yes.

Find x, the hypotenuse, when the side adjacent to a 52° angle is 9 m

  1. Sides involved: adjacent (9) and hypotenuse (x). Use cosine.
  2. cos 52° = .
  3. The unknown is on the bottom, so swap: x = = 9 ÷ 0.6157… = 14.62 m (to 2 decimal places).
  4. Sensible? 14.62 is longer than 9, as a hypotenuse must be.

Find the angle θ when the opposite side is 5 and the adjacent side is 8

  1. Sides involved: opposite and adjacent. Use tangent.
  2. tan θ = = 0.625.
  3. To undo tan, use the inverse: θ = tan−1(0.625) = 32.0° (to 1 decimal place).
  4. On most calculators this is SHIFT or 2nd followed by the tan key.

A 6 m ladder leans against a wall, making an angle of 70° with the ground. How high up the wall does it reach?

  1. Draw the triangle. The ladder is the hypotenuse (6 m). The height up the wall is opposite the 70° angle.
  2. Opposite and hypotenuse: use sine. sin 70° = .
  3. h = 6 × sin 70° = 6 × 0.9397… = 5.64 m (to 2 decimal places).
Common mistake: a calculator in radians mode. Test it: sin 30° should give 0.5. If you get −0.988, change the mode to degrees (look for D or DEG on the screen).
Common mistake: labelling opposite and adjacent from the wrong angle, or calling the hypotenuse the adjacent side because it touches the angle. The hypotenuse is always the side opposite the right angle; label it first, then find opposite and adjacent from the angle you are using.

Check yourself

  1. In a right-angled triangle, which side is opposite the right angle?
  2. Which ratio uses the opposite and adjacent sides?
  3. The side opposite angle θ is 7 cm and the hypotenuse is 10 cm. What is sin θ as a decimal?
  4. Find the side opposite a 40° angle when the hypotenuse is 15 cm (2 decimal places).
  5. Find the side opposite a 25° angle when the adjacent side is 10 m (2 decimal places).
  6. Find θ when the opposite side is 6 and the hypotenuse is 12.

Answers: 1. the hypotenuse 2. tangent 3. 0.7 4. 9.64 cm (15 × sin 40°) 5. 4.66 m (10 × tan 25°) 6. 30° (sin θ = 0.5)

worksheets.successtutoring.com · Free to print and share for personal and classroom use

Preview — the PDF contains the full resource.

More Year 9 trigonometry resources

  • Worksheet

    Year 9 Trigonometry (Finding Sides) Worksheet — Level 1

    Use sine, cosine and tangent to find unknown sides in right-angled triangles. Builds confidence with the core skill before adding…

    Difficulty
    Level 1 · Easier
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included
Was this resource helpful?

About this resource

Created by
Success Tutoring
Last reviewed
1 October 2026
How it was made
Written by our team

Free to print and share for personal, classroom and homeschool use. Please don't resell. Spotted an error? Let us know.