Everyday Math Essentials
Cover quick calculations for percentages, fractions, averages, and ratios used in school, shopping, and spreadsheets.
📐 Triangle Calculator
Calculate area, perimeter, angles, and all triangle properties
📏 Enter Measurements
📊 Results
Area
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Base
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Height
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📏 Enter Side Lengths
📊 Results
Area (Heron's Formula)
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Perimeter
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Semi-perimeter
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Angle A
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Angle B
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Angle C
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Height to A
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📏 Enter Measurements
📊 Results
Area
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Side C
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Perimeter
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Angle A
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Angle B
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📚 Understanding Triangles
What is a Triangle?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry and has many important properties. The sum of all interior angles in a triangle always equals 180 degrees.
Types of Triangles by Sides
- Equilateral Triangle: All three sides are equal in length, and all angles are 60°
- Isosceles Triangle: Two sides are equal in length, and two angles are equal
- Scalene Triangle: All three sides have different lengths, and all angles are different
Types of Triangles by Angles
- Acute Triangle: All three angles are less than 90°
- Right Triangle: One angle is exactly 90°
- Obtuse Triangle: One angle is greater than 90°
Triangle Formulas
Area (Base & Height): A = ½ × base × height
Area (Heron's Formula): A = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter
Area (SAS): A = ½ × a × b × sin(C)
Perimeter: P = a + b + c
Semi-perimeter: s = (a + b + c) / 2
Law of Cosines
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab × cos(C)
Law of Sines
The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C)
Practical Applications
- Construction: Calculating roof angles and support structures
- Navigation: Triangulation for determining positions
- Engineering: Structural analysis and design
- Surveying: Measuring distances and land areas
- Computer Graphics: 3D modeling and rendering
- Architecture: Designing triangular spaces and supports
Frequently Asked Questions
How do I calculate the area of a triangle?
The most common method is using base and height: Area = ½ × base × height. If you know all three sides, use Heron's formula. If you know two sides and the included angle, use: Area = ½ × a × b × sin(C).
What is Heron's formula?
Heron's formula calculates the area of a triangle when you know all three side lengths. First, find the semi-perimeter s = (a+b+c)/2, then Area = √[s(s-a)(s-b)(s-c)]. This method works for any triangle.
Can any three sides form a triangle?
No. The triangle inequality theorem states that the sum of any two sides must be greater than the third side. For example, sides of 3, 4, and 10 cannot form a triangle because 3 + 4 < 10.
What is the difference between acute, right, and obtuse triangles?
An acute triangle has all angles less than 90°. A right triangle has one angle exactly 90°. An obtuse triangle has one angle greater than 90°. Every triangle must be one of these three types.
How do I find the angles of a triangle if I know all three sides?
Use the Law of Cosines: cos(A) = (b² + c² - a²) / (2bc). Calculate this for each angle. Remember that the sum of all angles must equal 180°, which you can use to verify your calculations.
What is an equilateral triangle?
An equilateral triangle has all three sides equal and all three angles equal to 60°. It's a special case that is both equilateral (equal sides) and equiangular (equal angles). The area formula simplifies to: A = (√3/4) × side².
🧭 Guided Journeys
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These grouped paths are designed to help you continue with the most common follow-up calculations in this category.
Algebra & Equations
Move from powers and logarithms into more advanced solving tools when the problem gets more complex.
Geometry & Measurement
Calculate dimensions, area, and triangle relationships using a connected geometry workflow.