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Updated Mar 19, 2026

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8 pages

GCSE Maths 2023 Revision Guide: Part 2

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Right-angled triangles might seem tricky, but with the right tools,... Show more

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$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Pythagoras vs Trigonometry - When to Use Each

Pythagoras' theorem is brilliant for finding missing sides, but it can't help with angles. Trigonometry, on the other hand, is your go-to method when you need to find both missing sides and angles in right-angled triangles.

The Pythagoras formula is a² + b² = c², where c is always the longest side (hypotenuse). For example, if you have sides of 18m and 10m, the missing side equals √(18² - 10²) = √224 = 14.97m.

Quick Tip: Always check which information you're given - if you have two sides and need the third, use Pythagoras. If you have angles involved, you'll need trigonometry!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

SOHCAHTOA - Your Trigonometry Lifeline

SOHCAHTOA breaks down the three main trigonometric ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. This simple memory trick will save you in every triangle problem.

When you know an angle and need to find a side, multiply the trigonometric ratio by the known side. For instance, if you have a 35° angle and a 12cm hypotenuse, the opposite side = sin(35°) × 12 = 6.9cm.

Practice identifying which sides are opposite, adjacent, and hypotenuse relative to your given angle. Once you've got this sorted, choosing the right ratio becomes straightforward.

Remember: The hypotenuse is always the longest side, opposite the right angle. The opposite and adjacent sides change depending on which angle you're working with!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Unit Conversions Made Simple

Converting between metres, centimetres, and millimetres follows a clear pattern that you can master quickly. Each step up or down the scale involves multiplying or dividing by 10 or 100.

From metres to centimetres, multiply by 100 $7m = 700cm$ . From metres to millimetres, multiply by 1000 $13m = 13,000mm$ . Going the other way, you divide by the same amounts.

The key is remembering the scale: kilometres → metres (×1000) → centimetres (×100) → millimetres (×10). Once you've got this sequence down, you can convert between any units by combining the steps.

Pro Tip: Write out the units in order when you're stuck - it helps you see how many steps you need to take and in which direction!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Area Conversions - Think in Squares

Area conversions work differently because you're dealing with squared units. When converting 7cm² to mm², you need to think about how many millimetres fit in each centimetre direction.

Since 1cm = 10mm, then 1cm² = 10mm × 10mm = 100mm². Therefore, 7cm² = 700mm². The same logic applies to larger conversions - 1m² = 10,000cm² because 100cm × 100cm = 10,000cm².

For volume conversions, you're working with cubes, so the multipliers get even bigger. Converting 2m³ to cm³ means 2 × (100 × 100 × 100) = 2,000,000cm³.

Memory Trick: For area, square your conversion factor. For volume, cube it. So cm to mm (×10) becomes ×100 for area and ×1000 for volume!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Special Angles - The Magic Numbers

Certain angles appear so frequently in trigonometry that memorising their values will speed up your calculations enormously. 30°, 45°, and 60° are the key angles you need to know by heart.

For 45° triangles, sin and cos both equal 1/√2, while tan equals 1. 30° and 60° angles are connected - what's sin for one becomes cos for the other. Sin(30°) = 1/2 and cos(30°) = √3/2.

These special triangles often appear in exam questions, and recognising them instantly gives you a massive advantage. You won't need to reach for your calculator every time.

Exam Hack: If you see these angles in a question, there's usually a reason - the examiner expects you to use the exact values rather than decimal approximations!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Putting It All Together

You've now got all the tools needed to tackle any right-angled triangle problem. Pythagoras handles the pure side calculations, while SOHCAHTOA sorts out everything involving angles.

The secret to success is identifying what information you have and what you need to find. This determines whether you'll use sin, cos, tan, or Pythagoras' theorem.

Final Reminder: Practice makes perfect with these techniques. The more triangles you solve, the quicker you'll spot which method to use!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Updated Mar 19, 2026

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8 pages

GCSE Maths 2023 Revision Guide: Part 2

Wiki :)

@grav1ty.zer0

Right-angled triangles might seem tricky, but with the right tools, you'll be solving them like a pro! This guide covers Pythagoras' theorem and trigonometry- two powerful methods that help you find missing sides and angles in triangles you'll encounter... Show more

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Pythagoras vs Trigonometry - When to Use Each

Quick Tip: Always check which information you're given - if you have two sides and need the third, use Pythagoras. If you have angles involved, you'll need trigonometry!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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SOHCAHTOA - Your Trigonometry Lifeline

Practice identifying which sides are opposite, adjacent, and hypotenuse relative to your given angle. Once you've got this sorted, choosing the right ratio becomes straightforward.

Remember: The hypotenuse is always the longest side, opposite the right angle. The opposite and adjacent sides change depending on which angle you're working with!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Unit Conversions Made Simple

Converting between metres, centimetres, and millimetres follows a clear pattern that you can master quickly. Each step up or down the scale involves multiplying or dividing by 10 or 100.

From metres to centimetres, multiply by 100 $7m = 700cm$ . From metres to millimetres, multiply by 1000 $13m = 13,000mm$ . Going the other way, you divide by the same amounts.

Pro Tip: Write out the units in order when you're stuck - it helps you see how many steps you need to take and in which direction!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Area Conversions - Think in Squares

Area conversions work differently because you're dealing with squared units. When converting 7cm² to mm², you need to think about how many millimetres fit in each centimetre direction.

Since 1cm = 10mm, then 1cm² = 10mm × 10mm = 100mm². Therefore, 7cm² = 700mm². The same logic applies to larger conversions - 1m² = 10,000cm² because 100cm × 100cm = 10,000cm².

For volume conversions, you're working with cubes, so the multipliers get even bigger. Converting 2m³ to cm³ means 2 × (100 × 100 × 100) = 2,000,000cm³.

Memory Trick: For area, square your conversion factor. For volume, cube it. So cm to mm (×10) becomes ×100 for area and ×1000 for volume!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Special Angles - The Magic Numbers

Certain angles appear so frequently in trigonometry that memorising their values will speed up your calculations enormously. 30°, 45°, and 60° are the key angles you need to know by heart.

These special triangles often appear in exam questions, and recognising them instantly gives you a massive advantage. You won't need to reach for your calculator every time.

Exam Hack: If you see these angles in a question, there's usually a reason - the examiner expects you to use the exact values rather than decimal approximations!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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Putting It All Together

You've now got all the tools needed to tackle any right-angled triangle problem. Pythagoras handles the pure side calculations, while SOHCAHTOA sorts out everything involving angles.

The secret to success is identifying what information you have and what you need to find. This determines whether you'll use sin, cos, tan, or Pythagoras' theorem.

Final Reminder: Practice makes perfect with these techniques. The more triangles you solve, the quicker you'll spot which method to use!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

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We thought you’d never ask...

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Basil

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Sudenaz Ocak

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

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Elisha

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Paul T

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Stefan S

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Samantha Klich

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Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

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Basil

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David K

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Sudenaz Ocak

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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

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Elisha

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Paul T

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