All triangles have 3 sides and 3 angles which always add up to 180°.
The Triangle Inequality Theorem states that: Triangles are classified in 2 ways-
1) By the number of equal
sides they have:
2) By the types of
angles they have:
When these 2 categories are combined, there are 7 possible triangles:
• acute isosceles (diagram D)
• equilateral (G) all sides are equal and each angle = 60°, making this the
only equiangular triangle. Since all 3 angles are less than 90° all equilateral
triangles are acute triangles.
There is one more type of triangle that is worth mentioning.
1) The most well-known triangle area formula is multiplying the length of the base by the
height (also called the altitude), and dividing that by 2.
2) If you know the length of all 3 sides of a triangle, you can calculate the area by using
Heron's Formula (sometimes called Hero's Formula). A triangle's semi-perimeter (or 's') is one half of the perimeter or to put it another way:
Example: A triangle has side a = 4, side b = 5 and side c = 6. What is its area? area = square root (s • (s - a) • (s - b) • (s - c))
area = square root (s • (s - 4) • (s - 5) • (s - 6))
This is an easy formula to prove. First, we use the traditional formula: Area = ½ • height • base then we can substitute side 2 for the base: Area = ½ • height • side 2
Since sine (A) = height / side 1 then height = side 1 • sine(A)
This calculator determines triangle area by using any of the 3 methods above. |