•

1 Jan 2026

•

3 pages

Understanding SOHCAHTOA and Pythagoras' Theorem

Sehar

@ehar_oxdaozxefuetcct

SOHCAHTOA and Pythagoras' theorem are your best mates for solving... Show more

1 / 3

SOHCAHTOA

Opposite
Just the
90°

Hypotenuse - Always the longest
(4)
Side

Adjacent

On the line with
the marked angle
and the 90 angle

20

Understanding SOHCAHTOA

SOHCAHTOA is a memory trick that breaks down into three key ratios. Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. The hypotenuse is always the longest side, opposite the 90° angle.

Before diving into calculations, identify what you've got and what you need. If you have an angle and the opposite side but need the hypotenuse, you'll use sine. For example, if sin(35°) = 20/H, then H = 20 ÷ sin(35°) = 34.9cm.

When you need to find an angle instead of a side, use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹). If cos(x) = 16/24, then x = cos⁻¹(16/24) = 48.2°.

Top Tip: Always check which sides you can identify relative to your angle - this determines which ratio to use.

Solving Complex Triangle Problems

Real-world problems often require multiple steps and careful angle identification. When finding angle BAD in a complex shape, break it down into simpler right-angled triangles first.

Sometimes you'll need Pythagoras' theorem $a² + b² = c²$ before using SOHCAHTOA. If you've got two sides of a right triangle, Pythagoras finds the third. Then use trigonometry for the angles.

For tricky problems, work systematically. Find missing sides using Pythagoras first, then tackle the angles. Remember that angles in complex shapes might need adding or subtracting from each other.

Remember: When you see 25° and need angle BAD, you might need to add 90° + 7.6° = 97.6° depending on the triangle's orientation.

Mastering Pythagoras and Advanced Calculations

Pythagoras' theorem is brilliant for finding any side of a right-angled triangle when you know the other two. The hypotenuse (longest side) is always c in the formula c² = a² + b².

For complex problems involving multiple triangles, work step by step. Calculate intermediate lengths first, then use these to find your final answer. When finding diagonal AC in a rectangle, simply treat it as the hypotenuse of a right triangle.

Always give answers to the significant figures or decimal places asked for. Whether it's 1 d.p., 3 sig. fig., or exact values, check your calculator work and round appropriately.

Pro Strategy: Draw clear diagrams and label everything you know - it prevents silly mistakes and helps you spot which method to use.

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254

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1 Jan 2026

•

3 pages

Understanding SOHCAHTOA and Pythagoras' Theorem

Sehar

@ehar_oxdaozxefuetcct

SOHCAHTOA and Pythagoras' theorem are your best mates for solving right-angled triangles. Whether you need to find missing sides or angles, these tools will sort you out every time.

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Understanding SOHCAHTOA

When you need to find an angle instead of a side, use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹). If cos(x) = 16/24, then x = cos⁻¹(16/24) = 48.2°.

Top Tip: Always check which sides you can identify relative to your angle - this determines which ratio to use.

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Solving Complex Triangle Problems

Real-world problems often require multiple steps and careful angle identification. When finding angle BAD in a complex shape, break it down into simpler right-angled triangles first.

Sometimes you'll need Pythagoras' theorem $a² + b² = c²$ before using SOHCAHTOA. If you've got two sides of a right triangle, Pythagoras finds the third. Then use trigonometry for the angles.

For tricky problems, work systematically. Find missing sides using Pythagoras first, then tackle the angles. Remember that angles in complex shapes might need adding or subtracting from each other.

Remember: When you see 25° and need angle BAD, you might need to add 90° + 7.6° = 97.6° depending on the triangle's orientation.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Mastering Pythagoras and Advanced Calculations

Pythagoras' theorem is brilliant for finding any side of a right-angled triangle when you know the other two. The hypotenuse (longest side) is always c in the formula c² = a² + b².

Always give answers to the significant figures or decimal places asked for. Whether it's 1 d.p., 3 sig. fig., or exact values, check your calculator work and round appropriately.

Pro Strategy: Draw clear diagrams and label everything you know - it prevents silly mistakes and helps you spot which method to use.