# A Complicated Geometry Question (No, This Is Not Homework)
**URL:** https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689
**Category:** Factual Questions
**Created:** [June 8, 2018, 3:36pm UTC](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689 "2018-06-08T15:36:09Z")
**Posts on this page:** 4
**Page:** 2
### Author:  [@MrFloppy](https://boards.straightdope.com/u/MrFloppy)
#### Post date: [June 9, 2018, 7:09pm UTC](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689/21 "2018-06-09T19:09:14Z")
> [@bob\_2](#):
>
> This is beginning to look like a flat earth question
Yup. My Flerfer-Radar went straight into alert-mode.
---
### Author:  [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)
#### Post date: [June 9, 2018, 8:45pm UTC](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689/22 "2018-06-09T20:45:28Z")
By coincidence . i just watched a new report on the U2, and the pilot said the max range he can see above 60,000 ft is 260 nautical miles. And I was just reading this thread this morning. 🙂
---
### Author:  [@rat\_avatar](https://boards.straightdope.com/u/rat_avatar)
#### Post date: [June 9, 2018, 8:50pm UTC](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689/23 "2018-06-09T20:50:34Z")
> [@Chronos](#):
>
> You can’t get a rod that rigid, but you can get a straight laser beam. This is an issue, for the 10-km-long arms of the LIGO detectors.
>
> Note also that this question is equivalent to asking “how far away is the horizon, from a height of 1 m?”.
That is one case where it is easier to remember with imperial units.
```auto
_____________
1.17⋅╲╱ height(feet) = distance to horizon in NM
```
So at 1 Meter, 2.12 Nautical Miles or 2.12 minutes, which is probably just as easy to remember as:
```auto
______________
2.12⋅╲╱ height(meters) = minutes.
```
At least this is what I used when sailing in the pre-GPS days.
---
### Author:  [@rat\_avatar](https://boards.straightdope.com/u/rat_avatar)
#### Post date: [June 9, 2018, 10:06pm UTC](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689/24 "2018-06-09T22:06:10Z")
To clarify the above that had the multiplier to change units.find the distance to the horizon with the secant-tangent theorem.
Where:
D = diameter
R = radius
h = height
d = distance
```auto
___________
d = ╲╱ h⋅(D + h)
or:
_____________
d = ╲╱ h⋅(2⋅R + h)
```
These assume the same units so if the Diameter is 12742 KM or 12742000 Meters
d = 3569.594 Meters
But that finds the height at the intersection point, you would have to adjust for the right angle intersection in the OP, but I wanted to clarify the distance formula I was using above.
But it is not much more work to get the rest once you have this formula.
[Previous page](https://boards.straightdope.com/t/a-complicated-geometry-question-no-this-is-not-homework/815689.md?page=1)