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The triangle calculator helps you quickly determine unknown sides, angles, heights, medians, area, and more. It simplifies complex trigonometry calculations for students, teachers, and professionals.
The height can be calculated as:
\(\ h = \frac{2A}{b} \)
The area is determined by:
\(\ \text{Area} = \frac{1}{2} b h \)
If all three sides are known, Heron’s formula can be used:
\(\ s = \frac{a+b+c}{2} \)
\(\ \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \)
Triangles consist of three sides and three angles. You can calculate unknown values using the Pythagorean theorem, Law of Sines, or Law of Cosines.
The Law of Sines is useful for finding unknown sides or angles:
\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
For right triangles with known hypotenuse:
\(a = c \cdot \sin \alpha \quad\text{or}\quad a = c \cdot \cos \beta\)
\(b = c \cdot \sin \beta \quad\text{or}\quad b = c \cdot \cos \alpha\)
In right triangles, if two sides are known, the third can be found:
\(a^2 + b^2 = c^2\)
For unknown sides:
\(a = \sqrt{c^2 - b^2}\)
\(c = \sqrt{a^2 + b^2}\)
The Law of Cosines works for any triangle:
\(a^2 = b^2 + c^2 - 2bc \cdot \cos A\), so \(\cos A = \frac{b^2 + c^2 - a^2}{2bc}\)
\(b^2 = a^2 + c^2 - 2ac \cdot \cos B\), so \(\cos B = \frac{a^2 + c^2 - b^2}{2ac}\)
\(c^2 = a^2 + b^2 - 2ab \cdot \cos C\), so \(\cos C = \frac{a^2 + b^2 - c^2}{2ab}\)
If one side and one angle are known:
a = b \cdot \tan \alpha
b = a \cdot \tan \beta
If the area and one side are known:
b = \frac{2 \cdot \text{Area}}{a}
c = \sqrt{a^2 + (\frac{2 \cdot \text{Area}}{a})^2}
The inradius is the radius of the circle inscribed in the triangle:
\(r = \frac{\text{Area}}{s}\)
The circumradius is the radius of the circle passing through all triangle vertices:
\(R = \frac{a}{2 \sin A}\)
Given:
Step 1: Find the Third Angle
\(m\angle C = 180^\circ - A - B = 100^\circ\)
Convert angles to radians:
\(A = 1.0472 \text{ rad},\ B = 0.34907 \text{ rad},\ C = 1.74533 \text{ rad}\)
Step 2: Find Remaining Sides Using Law of Sines
\(b = \frac{a \cdot \sin B}{\sin A} = 0.78986\)
\(c = \frac{a \cdot \sin C}{\sin A} = 2.27432\)
Step 3: Calculate Area
\(A = \frac{ab \cdot \sin C}{2} = 0.77786\)
Step 4: Perimeter and Semiperimeter
\(p = a + b + c = 5.06418\)
\(s = \frac{p}{2} = 2.53209\)
Step 5: Heights
\(h_a = \frac{2A}{a} = 0.77786\)
\(h_b = \frac{2A}{b} = 1.96961\)
\(h_c = \frac{2A}{c} = 0.68404\)
Step 6: Medians
\(m_a = 1.37775, \ m_b = 2.10482, \ m_c = 1.00936\)
Step 7: Inradius
\(r = \frac{A}{s} = 0.3072\)
Step 8: Circumradius
\(R = \frac{a}{2 \sin A} = 1.1547\)
Other Languages: Výpočet Trojúhelníku, Calculer Triangle, Dreieck Rechner, Kalkulator Segitiga, Kalkulator Trójkata, Калькулятор Треугольника, Calcular Triangulo, Üçgen Hesaplama, Calculadora De Triángulos
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