Start of 3D Cone given base radius, height and centre of base position.

Question

So I have a maths assignment where two mosquitoes are travelling in 3D space and I have to find out a mathematical way to spray them. So far, I have analysed spray patterns and found a specific opening angle for a 3D cone, as well as a specific radius, then a specific height for the cone. However, I'm having trouble finding a starting point for the spray, and I have no clue how to approach it.
I have a plane $x+y=140$ then on this plane is the point $(\frac{17200}{273}, \frac{21020}{273}, \frac{13595}{273})$ which is to be the centre of the base of the cone (SprayCent in the image), which is on the plane. The cone is supposed to be at right angle to the plane.
Then, the radius of the cone base (r) is approximately 18.4 where the height (h) is approximately 101.45. I just need to find the starting point of this cone, thank you!
Here is a basic image of scenario

Answer 1

A perpendicular to the plane is the vector $(1,1,0)$ which you can normalize to $(\frac 1{\sqrt 2},\frac 1{\sqrt 2},0)$. You can measure either direction $18.4$ from your center point, so add or subtract $\frac {18.4}{\sqrt 2}$ from each of $x$ and $y$

Answer 2

So thank you to those who answered but I think I found a way.
SO, firstly I made two vectors where their starting points were the centre of the base of the cone. Then, I found the cross product of these vectors to produce a vector which was at right angles to the plane. Afterwards, this vector was normalised so that it had magnitude 1. Then, I multiplied this normalized vector by the height of the cone h and plugged it into GeoGebra to find the point where it ended, which then became the starting point of the cone.