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Geometry & Trigonometry

Geometry: Perimeters, areas, surface areas, and volumes of shapes.

Trigonometry: Lengths and angles of triangles.

Area and Perimeter






? The perimeter of an ellipse is an infinite series, so the Ramanujan approximation is used here








Volume and Surface area











Triangles

Triangles are defined by the length of the three sides and the three angles between them. To fully characterize a triangle, you need to know at least three of the six items. (If you only know the three angles, you also need at least one side to get the overall scale).

Law of sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Law of cosines: $$c^2 = a^2+b^2-2\,a\,b\cos(C) $$

Area (Heron's Formula): $$\textrm{half perimeter} = p = (a + b + c)\,/\,2 $$ $$\textrm{area} = \sqrt{p\,(p-a)\,(p-b)\,(p-c)}$$

For right triangles: $$\sin A=\frac{\textrm{opposite}}{\textrm{hypotenuse}}=\frac{a}{\,c\,}$$ $$\cos A=\frac{\textrm{adjacent}}{\textrm{hypotenuse}}=\frac{b}{\,c\,}$$ $$\tan A=\frac{\textrm{opposite}}{\textrm{adjacent}}=\frac{a}{\,b\,}=\frac{\sin A}{\cos A}$$

Drag the vertices of the triangle and see the effects!

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Check the boxes next to the three values to be calculated, enter the other three known values, and click "Calculate".

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