Step-by-step triangle tutorials: solving right triangles, finding area, checking answers, word problems, feet-and-inch math, and squaring footings.
12 articles
Trigonometry word problems step by step: a five-step method (draw, record, identify, choose the ratio, solve and check) with worked examples and practice.
Triangle area formula: A = ½ × base × height, so a 12 cm base and 8 cm height give 48 cm². Without the height, use ½ab sin C, Heron's formula or coordinates.
How to check your triangle answers: the 180° angle sum, Pythagorean and triangle inequality tests, Law of Sines ratios, area checks and a worked example.
Square, plumb and straight: what each term means, how to check it with a level, string line or the 3-4-5 method, worked numbers and typical tolerances.
How to square a ground-mounted solar array pier layout: diagonal targets from the Pythagorean theorem, a worked 8-pier example, and grid checks.
How to square building footings with the 3-4-5 method and a diagonal check: the math, a worked 24 × 36 ft garage layout, tolerances, and layout tools.
The unit circle is a radius-1 circle where each point is (cos θ, sin θ). Special angles, radians, ASTC signs, reference angles and practice problems.
Feet and inches in triangle math: convert to decimal feet or inches, handle fractional inches, and turn answers back into tape-measure readings.
Triangle inequality theorem: any two sides must add to more than the third. Plus the hypotenuse, Pythagorean, angle-sum and trig checks for your answers.
How to solve a right triangle from any two known values (at least one a side) with the Pythagorean theorem and sin, cos, tan, worked step by step.
Decimal place precision by job, from DIY (±⅛") to precision machining (±0.0001"): how many digits to keep, with worked right triangle examples.
Right triangle mistakes students make: wrong hypotenuse, missing square root, mislabeled angles, mixed units, early rounding. Each with an example and fix.
