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Triangle calculator

This calculator applies the Law of Sines $~~ \dfrac{\sin\alpha}{a} = \dfrac{\cos\beta}{b} = \dfrac{cos\gamma}{c}~~$ and the Law of Cosines $ ~~ c^2 = a^2 + b^2 - 2ab \cos\gamma ~~ $ to solve oblique triangles, i.e., to find missing angles and sides if you know any three of them.

The calculator shows all the steps and gives a detailed explanation for each step.

Oblique Triangle Calculator
input three values and select what to find
show 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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