Guides
Worked explanations of the geometry behind the calculator - written for people who want to understand the result, not just copy it.
Showing 1–12 of 15 guides
The 30-60-90 triangle rule: sides always sit in the ratio 1 : √3 : 2. Get the formulas, learn to rationalise √3, and follow eight fully worked examples.
Read the guideThe 45-45-90 triangle has sides in the ratio 1 : 1 : √2. Learn the rule, find the hypotenuse or a leg, simplify radicals, and work through 8 solved examples.
Read the guideSOHCAHTOA explained in full: SOH, CAH and TOA, how to name opposite and adjacent from your angle, and which ratio to pick for every right triangle problem.
Read the guideA Pythagorean triple is three positive integers with a² + b² = c². Get all 16 primitive triples up to hypotenuse 100, Euclid's formula and worked examples.
Read the guideThe 3-4-5 triangle rule makes an exact 90° corner using the converse of the Pythagorean theorem. Angles, scaling, unit examples, accuracy limits and practice.
Read the guideThe right triangle altitude theorem states h² = p · q. See the statement, the three similar triangles, a full proof, the leg theorem and seven worked examples.
Read the guideThe angle of elevation is measured up from the horizontal, the angle of depression down from it. Learn both with 11 solved right triangle problems and diagrams.
Read the guideTwenty right triangle word problems solved step by step: ladders, ramps, shadows, guy wires, diagonals, angles of elevation and depression, plus multi-step.
Read the guide5² + 12² = 169 = 13², so 5-12-13 is a right triangle. Exact angles, area, altitude, scaled versions, trig ratios and six worked examples with full working.
Read the guideThe geometric mean of x and y is √(xy). See how the altitude and legs of a right triangle become geometric means, and solve 12 worked problems step by step.
Read the guideFind an angle of a right triangle from two sides: form the ratio, apply sinâ»Â¹, cosâ»Â¹ or tanâ»Â¹, and read the result in degrees. Ten worked examples and practice.
Read the guideTwo right triangles are similar if one pair of acute angles matches. AA similarity, correspondence order, proportions, scale factor, the altitude case and 9 examples.
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