Question

Find the three dimensional diagonals. Round to the nearest tenth. I=5.1 w=8.5 h=5.8 first diagonal (on the base): second diagonal (cutting through the figure):

Answer 1

To find the diagonals we use the pythagorean theorem:

$c^2=a^2+b^2$

in each case the diagonal is the hypotenuse of the triangle.

For the base diagonal we have that the legs of the triangle are l and w, then we have:

$\begin{gathered} c^2=5.1^2+8.5^2 \\ c=\sqrt[]{5.1^2+8.5^2} \\ c=9.9 \end{gathered}$

Therefore the base diagonal is 9.9

Now, the second diagonal is the hypotenuse of the triangle with legs h and base diagonal, then we have that:

$\begin{gathered} d^2=9.9^2+5.8^2 \\ d=\sqrt[]{9.9^2+5.8^2} \\ d=11.5 \end{gathered}$

Therefore the second diagonal is 11.5