Right-angled trigonometry | SOHCAHTOA worksheets

Teach right-angled trigonometry through a similar-triangle investigation, worked examples and scaffolded worksheets. Students discover why sine, cosine and tangent ratios work, then find missing sides and angles and apply their learning to a tower-height problem.

Designed for Years 10–11 (ages 14–16) maths learners who already understand ratios, similar triangles and basic equation rearrangement. A scientific calculator in degree mode is required. The suggested sequence covers two lessons of approximately 50–60 minutes each; teachers can also select individual sections for review or intervention.

What is included
• Seven student pages: a ratio investigation, clear side definitions, sine/cosine/tangent reference, worked side and angle examples, nine numbered practice/application/reasoning questions, quick checks and a four-part exit check.
• Two separate homework pages: six fresh questions covering sine, cosine, tangent, a missing hypotenuse, an angle and ladder-height error analysis. Suggested use is 15–20 minutes, or split after the two lessons.
• Four teacher/answer pages, including the homework worked answers: suggested lesson sequence, discussion prompts, responses to common errors, support and extension suggestions, and full worked answers.
• Matching colour and printer-friendly editions in PDF and editable Microsoft Word format: four files, each containing the same thirteen-page teaching pack.

Students use SOHCAHTOA, rearrange equations when the hypotenuse is unknown, use inverse trig functions to find acute angles, and solve an angle-of-elevation problem that accounts for the observer’s eye height. Rotated diagrams and error analysis help check understanding beyond copying a procedure. Each calculation is supported by a numerical check or sensibleness test.

This resource covers right-angled triangles with acute reference angles. It does not cover the sine rule, cosine rule, unit circle, radians or a full trigonometry unit. Diagrams are not to scale; all required measurements are supplied. No cutting, measuring equipment, online account or special app is required. Print on A4, or use your printer’s fit-to-page option if printing on another paper size.

The PDF preserves the page layout. The DOCX files let you adapt the text; Microsoft Word or compatible software is needed for editing, and edits may change pagination. The diagrams are embedded images. For economical printing, select grayscale or black ink only in your printer settings.

Optional free companions
The OpenLatitude SOHCAHTOA exercise sheet with worked answers and the one-page Trigonometry Quick Reference are separate free companion resources. They can be used independently; no purchase is required. These free pages are not counted in this paid pack’s 13 pages. Find them in the OpenLatitude shop under those titles.

Quality study materials designed to work in any classroom, anywhere in the world.

OpenLatitude. Licensed for single classroom use.