Question 1

How do I calculate the area of a triangle?

Accepted Answer

The simplest formula is A = 1/2 x base x height. If you know all three sides, use Heron's formula: find the semi-perimeter s = (a+b+c)/2, then A = sqrt(s(s-a)(s-b)(s-c)). If you know two sides and the included angle, use A = 1/2 x a x b x sin(C).

Question 2

What is Heron's formula?

Accepted Answer

Heron's formula calculates the area of a triangle from the lengths of its three sides. First compute the semi-perimeter s = (a+b+c)/2, then A = sqrt(s(s-a)(s-b)(s-c)). It is named after Hero of Alexandria and works for any triangle without needing to know the height.

Question 3

What is the triangle inequality theorem?

Accepted Answer

The triangle inequality theorem states that the sum of any two sides of a triangle must be strictly greater than the third side. If a + b <= c for any arrangement of sides, no valid triangle exists. This is a fundamental constraint that this calculator checks before computing.

Question 4

How do I determine what type of triangle I have?

Accepted Answer

Compare the side lengths: if all three are equal, it is equilateral. If exactly two are equal, it is isosceles. If all three differ, it is scalene. For angle classification, use the Pythagorean relationship: if a^2 + b^2 = c^2 (with c being the longest side), it is right. If a^2 + b^2 > c^2, it is acute. If a^2 + b^2 < c^2, it is obtuse.

Question 5

How do I find the height of a triangle from three sides?

Accepted Answer

First calculate the area using Heron's formula. Then use h = 2A / b, where b is the base you want the height relative to. For example, if sides are 5, 6, 7: s = 9, A = sqrt(9x4x3x2) = sqrt(216) = 14.697, and height from side 7 is h = 2(14.697)/7 = 4.199.

Triangle Calculator

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