Mathematics classroom notes
Year 10 - Bearings, angles of elevation and depression
Strand / topic: Measurement and Geometry / Bearings, angles of elevation and depression
Based on Pi Leo Academy's Victorian Curriculum F-10 Mathematics year-level guide and aligned to NAPLAN-style mathematical reasoning. Official curriculum code: Not stated in the provided curriculum source.
By the end of this note, students should be able to explain bearings, angles of elevation and depression, use a clear method, solve simple and test-style questions, and check their answers for Year 10 Measurement and Geometry work.
It helps with heights, distances, navigation, design and senior maths preparation. This topic builds the reasoning, fluency and confidence students need for future NAPLAN-style questions and everyday mathematics.
Which side and angle are connected?
Trigonometry links angles with side lengths in right-angled triangles.
If you know an angle and one side, a trig ratio can help find another side.
For Year 10, focus on understanding the idea before rushing to the final answer.
Think about it: ramps, ladders, heights and distances can use trigonometry.
Use this visual to organise bearings, angles of elevation and depression before calculating.
Label sides from the chosen angle.
What you need to know for this topic
Use this as a study checklist before trying quizzes, worksheets or NAPLAN-style questions.
Right triangles
- hypotenuse
- opposite
- adjacent
- chosen angle
Ratios
- sine
- cosine
- tangent
- calculator degree mode
- rounding answers sensibly
1 What this means
Trigonometry connects angles and side lengths in right-angled triangles. Start by learning to label the sides relative to the chosen angle before selecting sine, cosine or tangent. A helpful visual is a right-angled triangle with opposite, adjacent and hypotenuse labelled. For example, this idea can be used when finding an inaccessible height or distance.
Trigonometry connects angles and side lengths in right-angled triangles. In Year 10, students should first ask, 'What is the question really asking me to find?' Then they can draw a picture, make a table, use a number line, write a formula or build an equation. The final answer should match the story, the units and the size of the numbers.
- Confirm the triangle is right-angled.
- Label opposite, adjacent and hypotenuse from the chosen angle.
- Choose sine, cosine or tangent after labelling the sides.
- Use degree mode unless the question says otherwise.
2 Important rules / ideas
Basic sine, cosine and tangent are for right-angled triangles.
Opposite and adjacent depend on the chosen angle.
Use degree mode for school angle questions unless told otherwise.
Important vocabulary
The longest side of a right-angled triangle.
The side across from the chosen angle.
The side next to the chosen angle, not the hypotenuse.
A comparison used in sine, cosine and tangent.
3 Step-by-step method
- Mark the right angle and chosen angle.
- Label opposite, adjacent and hypotenuse.
- Choose sine, cosine or tangent.
- Solve and check the size of the answer.
4 Worked examples
In a right triangle, identify the hypotenuse.
- The hypotenuse is opposite the right angle.
- It is always the longest side.
If opposite = 6 and hypotenuse = 10, find sin(theta).
- sin(theta) = opposite / hypotenuse.
- sin(theta) = 6/10 = 0.6.
Find x if tan(35 degrees) = x/12.
- Multiply both sides by 12.
- x = 12 x tan(35 degrees).
- Use a calculator and round as required.
A ladder leans against a wall, making a right triangle. Which maths helps find the height?
- Right-angled trigonometry connects sides and angles.
- Choose sin, cos or tan based on the known information.
5 More examples
Opposite 4, hypotenuse 8.
sin(theta) = 4/8 = 1/2.
Known adjacent and hypotenuse.
Cosine connects adjacent and hypotenuse.
NAPLAN-style thinking
In NAPLAN-style questions, bearings, angles of elevation and depression may appear as a short calculation, a word problem, a diagram, a table or a multi-step reasoning question. Students should slow down and decide what the question is really asking before calculating.
Estimate first and eliminate answers that are too small, too large or use the wrong unit.
Write only the answer required, but use working on paper to avoid mental slips.
Circle the numbers, underline the action words and decide whether all numbers are needed.
Do one step at a time and label intermediate answers so the final step is clear.
6 Common mistakes
Label opposite, adjacent and hypotenuse from the chosen angle.
Use degrees for school angle questions unless told otherwise.
Keep extra decimals until the final answer.
- Choosing the first operation seen in the wording.
- Forgetting units, labels or place value.
- Stopping after the first step when the question asks for a final comparison.
7 Tips to remember
The ratio choice comes after side labels.
Check for a right angle before using SOH-CAH-TOA.
Rounding too early changes the final answer.
Parent teaching tips
- Ask your child to explain the method aloud before writing the answer.
- Use a real-life context at home, such as shopping, cooking, sport scores, maps or timetables.
- Praise clear working and checking, not only speed.
- Ask your child to write the formula or rule first, then substitute values carefully.
Remember
Label the triangle from the chosen angle before choosing sin, cos or tan.
8 Quick practice
- In a right triangle, identify the hypotenuse.
- If opposite = 6 and hypotenuse = 10, find sin(theta).
- Find x if tan(35 degrees) = x/12.
- A ladder leans against a wall, making a right triangle. Which maths helps find the height?
9 Answers / explanation
Question 1
Answer: It is always the longest side.
The hypotenuse is opposite the right angle. It is always the longest side.
Question 2
Answer: sin(theta) = 6/10 = 0.6.
sin(theta) = opposite / hypotenuse. sin(theta) = 6/10 = 0.6.
Question 3
Answer: Use a calculator and round as required.
Multiply both sides by 12. x = 12 x tan(35 degrees). Use a calculator and round as required.
Question 4
Answer: Choose sin, cos or tan based on the known information.
Right-angled trigonometry connects sides and angles. Choose sin, cos or tan based on the known information.
Extension challenge
Create your own multi-step question for this topic using an Australian context, then solve it and explain each step.
Hint: Use shopping, sport, maps, timetables, weather, school events or measurement at home.
Answer guide
Answers will vary. A strong answer includes clear working, correct units and a final sentence.
Quick revision
- Know what bearings, angles of elevation and depression is asking you to find.
- Choose a diagram, table, formula, number line or equation before calculating.
- Show enough working that you can find and fix mistakes.
- Check the final answer, units and reasonableness.