Solids > Calculations
12345Calculations

## Theory

In order to calculate the length of line segments and the size of angles you look for suitable planes in the 3D figure. draw these planes (life size if you like). Add the data and calculate the requested length and or angle.

Most of the time you look for suitable right triangles, for in those you can use:

• Pythagoras' theorem: ${c}^{2}+{a}^{2}={b}^{2}$ .

• The goniometric ratios:

• $\mathrm{sin}\left(\alpha \right)=\frac{a}{b}$

• $\mathrm{cos}\left(\alpha \right)=\frac{c}{b}$

• $\mathrm{tan}\left(\alpha \right)=\frac{a}{c}$

Note that in this case $b$ is the hypothenuse, $a$ the cathetus facing angle $\alpha$ and $c$ the adjacent cathetus for angle $\alpha$ .

You often use uniformity: two figures are uniform if they have equal angles and the edges are proportional. All edges of one figure can be obtained form the other figure by multiplication with the same scaling factor.