Trigonometry: Finding Lengths and Angles — Interactive Lesson (Ages 14–16)

Struggling to choose between sine, cosine and tangent? This interactive trigonometry lesson guides students from labelling the sides of a right-angled triangle to finding missing lengths and angles.

Mastering Trigonometry in Year 10–11 Maths

Students start by labelling the opposite, adjacent and hypotenuse sides with a drag-and-drop activity, then learn how sine, cosine and tangent are defined and why the ratios stay the same for any triangle with the same angle. They practise using a calculator to 3 significant figures, work through worked examples such as a ladder leaning against a wall, and finish by finding angles when two sides are known.

What’s Included

• Interactive trigonometry lesson with activities
• Learning objectives on applying trigonometric ratios to find angles and lengths
• Drag-and-drop labelling of the opposite, adjacent and hypotenuse sides
• Calculator practice and the exact values of sin, cos and tan for 0°, 30°, 45° and 60°
• Worked examples finding lengths, such as a 5 m ladder at 70° to the ground

Key Benefits for Students

• Makes choosing the correct ratio a clear, repeatable step
• Builds calculator skills, including working in degree mode
• Covers both finding lengths and finding angles
• Feedback on questions shows straight away whether an answer is right

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• Worked examples model how to set out each calculation
• Answers can be written in books, so it works as a lesson or homework
• A natural follow-on from Pythagoras theorem

Love this? You’ll love…

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A dependable addition to a GCSE geometry topic, giving students a clear routine for choosing the right ratio and setting out their working. Confidence here supports the harder triangle problems that follow.

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FAQ

What year group is this for? Years 10–11 (ages 14–16).

Does it cover finding angles as well as lengths? Yes — it covers finding lengths and finding angles in right-angled triangles.

Do students need a calculator? Yes — the lesson includes calculator activities.