(Solved): Find the lengths of the sides of the triangle ABC with the indicated vertices. A(6,0,0)B(0,10,0)C(0 ...

Find the lengths of the sides of the triangle $ABC$ with the indicated vertices. $\begin{array}{l}A(6,0,0)\\ B(0,10,0)\\ C(0,0,-16)\end{array}$ Step 1 Let $A(6,0,0),B(0,10,0)$, and $C(0,0,-16)$ be the vertices of the triangle $ABC$ To find the length of each side of the triangle, use the distance formula for the length of the segment between two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$. $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$ Find the length of the side $AB$ by using the distance formula. $\begin{array}{rl}|AB|& {=\sqrt{(0-6{)}^2+(10-0{)}^2+(-16}\times -(0))}^2\\ & =\sqrt{(6{)}^2+(10{)}^2+(}\times \frac{1}{\times {)}^2}\end{array}$