A mathematician, physics professor and a doper are asked to determine the height of a tower, for this task they receive a thermometer
The mathematician notes that the markings on the thermometer are exactly 1cm apart:
Walks away from the tower until he can make Equilateral triangle with the tower silhouette, using the Pythagoras’ theorem he figures the hight without to much difficulty

Our physics professor climbs the tower and drops the thermometer from the ledge, counting the seconds until it hits the ground, and with gravitational) he easily culculatates the towers height
How did the doper solve it?

My submission

The doper walks into the nearest pub, asks if he can trade this spiffy thermometer for a drink, and asks casually…”hey anyone know how high that tower is?

In the original joke it’s important that the instrument be a barometer. The trick to the trick question is that barometers have been used to measure altitude, but they are inaccurate, due to vagaries of air temperature and pressure. edit: Hence, students who answer “measure the air pressure to determine the building’s height” are not giving a good answer.

The gag answer was like yours, “Walk down to the basement and offer the building super this nifty barometer for a look at the plans.”

I didn’t catch that when I read the OP. If someone told “Measure the height of that building using this.” and handed me a thermometer, I’d think “What the hell are you expecting me to do with this?”

Doper 1: Since we know that temperature decreases as altitude increases, and if it’s a very accurate thermometer then we can determine the temperature differential between the base and the top. Convert from degrees to feet.

Doper 2: Cite?

Doper 1: I saw it on The Discovery Channel.

Doper 3: You sure it wasn’t The Weather Channel?

Doper 4: I don’t watch TV, but , hot air rises meaning that it will be cooler at the base than the top.

Doper 3: It’s the same formula, you just have to use a negative value where a positive value was used and then multiply by -1. And the mods don’t like me.

Now I, personally, having a thermometer instead of a barometer, would climb to the top, tie a string on the thermometer, lower it to the ground and then measure how much string I used.