Trigonometry basics
Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem
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In a right triangle, sine compares opposite to hypotenuse, cosine compares adjacent to hypotenuse, and tangent compares opposite to adjacent: SOH CAH TOA. The ratio must match the known and unknown sides. Inverse sine, cosine, or tangent finds an angle when the side lengths are known.
Spend 15 minutes labeling a right triangle, choosing the correct ratio, and solving one side problem and one angle problem with a calculator in degree mode.
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PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
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Area Builder supports hands-on exploration for Trigonometry basics. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
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Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Identify which trigonometric ratio to use (SOH CAH TOA) based on the known and unknown sides
- Calculate an unknown side using sin, cos, or tan and a known angle
- Find an unknown angle using the inverse trigonometric function (e.g. tan⁻¹)
“If your child knows a ladder is 5 metres long and leans against a wall at 70° to the ground, can they use trigonometry to work out how high up the wall it reaches?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 13–15
Standards