Mathematics Articles - Trigonometry Blog

Diagram of an equilateral triangle showing equal sides, 60-degree angles, and symmetry lines with mathematical annotations

Equilateral Triangles: The Perfect Triangle Explained

Equilateral triangle: three equal sides, three 60° angles. Height (√3/2)s, area (√3/4)s², the 30-60-90 link, a table of common sizes and worked problems.

Diagram showing an oblique triangle with labeled sides and angles illustrating the Law of Sines formula a/sin(A) = b/sin(B) = c/sin(C)

Mathematics 8 min read

Law of Sines Explained: When and How to Use It

The Law of Sines, a/sin A = b/sin B = c/sin C, solves non-right triangles in AAS, ASA and SSA cases. When to use it, worked examples, the ambiguous case.

Geometric diagram showing perpendicular lines in a triangle with height and base measurements highlighted for area calculation

Mathematics 5 min read

Perpendicular Lines and Why They Matter for Area

Perpendicular lines and area: the height in ½ × base × height must meet the base at 90°. Why, how to find it in any triangle, and measuring examples.

Geometric shapes showing different triangle area calculation methods and formulas

Mathematics 10 min read

Triangle Area Formulas: Heron's Formula & 5 Other Methods

Triangle area formulas compared: Heron's formula for three sides, ½ab sin C, base × height, coordinates and the 3D cross product, and when each one fits.

Collection of acute, right, and obtuse triangles showing geometric classification

Mathematics 8 min read

3 Types of Triangles: Acute, Right & Obtuse - When to Use Each

Acute, right and obtuse triangles: tell them apart with the a² + b² vs c² test, and see which formulas (SOH-CAH-TOA, Law of Cosines, Heron's) fit each.

Unit circle diagram showing relationship between angles, coordinates, and trigonometric ratios

Mathematics 12 min read

Unit Circle Explained: How Right Triangles Connect to Trig Functions

The unit circle explained through right triangles: with a hypotenuse of 1, sine is the y-coordinate and cosine the x-coordinate, for any angle.

Geometric pattern showing 30-60-90 and 45-45-90 special right triangle ratios

Mathematics 9 min read

30-60-90 & 45-45-90 Triangles: Special Right Triangle Guide

30-60-90 and 45-45-90 triangles: side ratios 1 : √3 : 2 and 1 : 1 : √2, why they hold, how to remember them, and worked examples with answers.

Protractor and compass tools for measuring angles in degrees and radians

Mathematics 8 min read

Degrees vs Radians: Angle Measurement Systems Explained

Degrees vs radians: 180° = π radians, so multiply by π/180 to get radians and by 180/π to get degrees. Conversion table, when to use each, common mistakes.

Mathematical grid displaying common Pythagorean triples like 3-4-5 and 5-12-13

Mathematics 10 min read

Pythagorean Triples: Perfect Integer Right Triangles (3-4-5 & More)

Pythagorean triples are right triangles with whole-number sides, like 3-4-5 and 5-12-13. A list of common triples, Euclid's formula, scaling and patterns.

Right triangle diagram illustrating the Pythagorean theorem with sides labeled a, b, and c

Mathematics 12 min read

Pythagorean Theorem Explained: History, Proofs & Modern Applications

The Pythagorean theorem a² + b² = c² explained: what it says, why it holds only with a right angle, its history from Babylon to Euclid, and three proofs.