Easy math puzzles

To determine the width of the tank from a single point, no measured angles, I think you’d need to know the distance to the tank. Then you could do it by measuring how much of a fixed object (at a fixed distance) it blocks from sight

Quote: Ace2

To determine the width of the tank from a single point, no measured angles, I think you’d need to know the distance to the tank. Then you could do it by measuring how much of a fixed object (at a fixed distance) it blocks from sight
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I don't think you could do it without measuring angles, being you can only see the endpoints of a perpendicular diameter across the tank at infinity.

There are ways to measure radii of curvature optically, like the way you would inspect a lens or curved mirror. If I had a lens bench and some sample lenses I could do it. Might even be able to do it with a surveyor's transit, see what I have to do to keep the telescope in focus when looking at a different point on the tank.

The surface of the tank makes a difference too. If there were markings or gradations on the tank that would help, even if it was just a chip in the paint. If it was a perfectly uniform Lambertian surface all around there would be no visual distinction between any two points on the tank, not sure what you would do.

Quote: Ace2

To determine the width of the tank from a single point, no measured angles, I think you’d need to know the distance to the tank. Then you could do it by measuring how much of a fixed object (at a fixed distance) it blocks from sight
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The method you suggested using a base line and the Sine Rule is mathematically valid but is unlikely to be used in practice due to the potential introduction of errors.

No data was provided because it forces the reader to solve the problem from first principles. The question asks for the radius, which, in this case, is defined by a formula. To answer this question from a single external standpoint the Secant Distance can be defined as SD and the included angle at the centre of the tank (between the radial lines tangential to where the LHS and RHS bearing lines intersect with the tank) can be defined as Theta.

The Secant Distance is the shortest horizontal distance from your standpoint to the tank. In an actual example, it is measured from the mean of the LHS and RHS bearings. Then add the radius, R, and you define the centre of the tank.

The angle between the LHS and RHS bearings at the standpoint is defined as 2*(180° – (90° + Theta/2)).

^^^
Please provide a numerical example including a diagram

Quote: Ace2

^^^
Please provide a numerical example including a diagram
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Ok, but in a few days so other readers have a chance to solve it.