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Triangle calculator

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This calculator uses the Law of Sines and the Law of Cosines to solve oblique triangles, i.e., to find missing angles or sides if you know any three of them. Provide any three triangle properties to find the missing side, angle, or area. The calculator shows all the steps and gives a full explanation for each step.

Triangle Calculator
input three elements of an acute or obtuse triangle, then choose a missing value
help ↓↓ examples ↓↓
The missing value is:
Input three elements of a triangle:
calculator works with decimals, fractions and square roots (to input $ \color{blue}{\sqrt{2}} $ type $\color{blue}{\text{r2}} $)
$ a $
=
$ b $
=
$ c $
=
$ \alpha $
=
$ \beta $
=
$ \gamma $
=
Area
=

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Oblique triangle formulas
$$ A = \frac{a\,b\,\sin\gamma}{2} $$
area
$$ A = \frac{b\,c\,\sin\alpha}{2} $$
area
$$ A = \frac{a\,c\,\sin\beta}{2} $$
area
$$ c^2 = a^2 + b^2 - 2ab \cos \gamma $$
law of cosines
$$ b^2 = a^2 + c^2 - 2ac \cos \beta $$
law of cosines
$$ a^2 = b^2 + c^2 - 2 b c \cos \alpha $$
law of cosines
 
$$ \frac{a}{\sin\alpha} = \frac{b}{\sin\beta} = \frac{c}{\sin\gamma} $$
law of sines
 
EXAMPLES
example 1:ex 1:
A triangle has sides equal to $ 3 m $, $5 m$ and $6 m$. Find angle $\alpha$ using cosine theorem.
example 2:ex 2:
Using the sine theorem, find the length of side c.
Sine and cosine law problem
example 3:ex 3:
Find angle $\beta$.
Sine and cosine law problem
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