Will a rectangular truck fit into a half circle formed tunnel when

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A truck with a width of 2.40 meters and a height of 3.41 meters is attempting to pass through a half-circle tunnel with a radius of 3.60 meters. The discussion highlights the use of the Pythagorean theorem to determine if the truck can fit, revealing that the height at the tunnel's center is only 3.39 meters. The conclusion is that the truck will not fit due to its height exceeding the tunnel's available height. The original poster expresses frustration over their inability to solve the problem despite having a background in higher mathematics. Ultimately, the conversation reflects on the challenges of focusing and understanding geometry concepts.
gocuriosity
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A truck with a width of 2,40 and height of 3,41 is driving through a tunnel that is formed like a half circle and has the radius of 3,60. Will it work?

Now, this is a very pathetic question because this is junior high level geometry. I could blame the incapacity to solve this question on weariness and whatnot, yet the truth is that I suck at math, lol.

I drew a picture of this but can't get it right whatever I do. I googled the question and people have been giving explanations on how to solve it, such that I don't understand. I'm guessing that you have to use the pythagorean theroem.

According to the textbook, the correct answer is that it won't go too well because the height of the tunnel 1,20 from the center is 3,39. (1,20 being equal to 2,40/2, what is sticking out of the truck to the sides, assuming it's driving in the center of the road.

I really have no clue how to solve this.

Thank you all!
 
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No actually, it's alright. I really have no clue what was going on in my head...

3.60^2 = 1,20^2 + x^2
x^2= 12,96 - 1,44
x = sqrt(12,96 - 1,44)
x = approximately 3,39

Again, I really have no idea how I couldn't see right away that the radius = hypotenuse. I've taken classes in calculus, trig etc and passed the classes without doing a thing. I wasn't getting A's that way, however I understand those topics of mathematics.

Is it possible to be so tired and unfocused to not see the solution to that question? Maybe that's a question for a psychiatrist.

thanks anyway to you all!
 
hi gocuriosity! welcome to pf! :smile:

look at your picture: the centre of the bottom of the truck is at the centre of the circle

so the radius of the circle must be greater than … ? :wink:

EDIT: oh, you've done it! :biggrin:
 
Yeah I did it... and I really don't know what was going on in my mind when I just couldn't see the solution. :)

Sorry for posting in the wrong section!
 

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