Triangle ماشینحساب
از Triangle ماشینحساب برای دریافت نتایج سریع و دقیق استفاده کنید.
نحوه استفاده از این ماشین حساب
- Side A را وارد کنید
- Side B را وارد کنید
- Side C را وارد کنید
- روی دکمه محاسبه کلیک کنید
- نتیجه نمایش داده شده در زیر ماشین حساب را بخوانید
How to Calculate Triangle Properties
A triangle is defined by three sides and three angles that always sum to 180 degrees. Given enough information (at least 3 values including one side), you can calculate all remaining properties using trigonometric laws.
The Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). The Law of Cosines: c² = a² + b² − 2ab×cos(C). These two laws, combined with the 180-degree rule, solve virtually any triangle problem.
Triangle Area Formulas
Multiple formulas exist depending on what you know:
- Base × Height: A = ½ × b × h (most intuitive)
- Two sides + included angle: A = ½ × a × b × sin(C)
- Heron's formula (three sides): A = sqrt(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
Heron's formula is particularly useful when you know all three sides but no heights or angles.
Special Triangles
Equilateral: All sides equal, all angles 60 degrees. Area = (sqrt(3)/4) × side². Isosceles: Two equal sides, two equal base angles. Right triangle: One 90-degree angle, governed by the Pythagorean theorem (a² + b² = c²). 30-60-90 triangle: Sides in ratio 1 : sqrt(3) : 2. 45-45-90 triangle: Sides in ratio 1 : 1 : sqrt(2).
Frequently Asked Questions
How do I find a missing angle?
Since all angles sum to 180 degrees, subtract the known angles from 180. If you know two sides and an angle, use the Law of Sines or Law of Cosines to find the remaining angles.
What is the Pythagorean theorem?
For right triangles only: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle). Example: a 3-4-5 triangle (3² + 4² = 9 + 16 = 25 = 5²).
Can a triangle have two right angles?
No. A triangle's angles must sum to exactly 180 degrees. Two right angles would use 180 degrees, leaving 0 for the third angle, which is impossible.
💡 آیا میدانستید؟
- The Pythagorean theorem (a²+b²=c²) was known in ancient Babylon and Egypt over 1,000 years before Pythagoras — a clay tablet from ~1800 BC lists Pythagorean triples.
- A triangle is the stiffest of all geometric shapes — the only polygon that cannot be deformed without changing the length of a side. That's why trusses and bridges use triangles.
- The sum of angles in any triangle always equals exactly 180° — but only in flat (Euclidean) geometry. On a sphere, the sum exceeds 180°.
آخرین بهروزرسانی: March 2026