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Triangle calculator
This solver uses the Law of Sines, and the Law of Cosines to solve acute and obtuse triangles , i.e., to find missing angles or sides if you know any three of them. Provide any three triangle properties of an oblique triangle to find the missing side, angle or area. The calculator shows all the steps and gives a full explanation for each step.
working...
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
ex 1:
A triangle has sides equal to $ 3 m $, $5 m$ and $6 m$. Find angle $\alpha$
using cosine theorem.
ex 2:
Using the sine theorem, find the length of side c.
ex 3:
Find angle $\beta$.
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