Strange Guys
In this mathematical problem, two tall vertical masts on level ground with guy ropes tethered cross at a point. Discover why the distance between the masts is irrelevant to determining the height at which they cross. The explanation involves the concept of similarity in triangles and how the scenario remains unchanged even if the diagram is stretched or transformed. Dive into the intriguing math behind this scenario and understand the reasoning behind the solution.
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Presentation Transcript
Strange Guys Source: various maths texts!
Strange Guys 900 ? 100 ? Not to scale ? 350 ? Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the other s base. They cross at a point between them. How high above the ground do they cross?
Strange Guys ? ? ? ? From similar triangles: Rearranging: Adding gives: ?=? ? ?=? ?and ? ? = ? ? ? = ? ?and ? ? = ? ?+ ? ?
Strange Guys ? ? ? ? ? = ? ?+ ? ?? ?+? So = ? Notice that the distance between the masts is irrelevant to the question asked. 1 ?+1 ? = ? 1 =1 ?+1 Or ? ? ?+? ?? 1 =
Strange Guys ? ? ? For: ? = 100 ? = 900 =(100) 900 100+900= 90 The guys cross 90 ? above the ground.
Strange Guys ? ? ? Can you simply explain why the distance ? is irrelevant? Imagine the diagram was printed on a rubber sheet and then stretched parallel to the ground.
Strange Guys ? ? Can you simply explain why the distance ? is irrelevant? Imagine the diagram was printed on a rubber sheet and then stretched parallel to the ground. You can see that is unaltered by the transformation. Note also that the ratio ?:? is unaltered.
Strange Guys 900 ? 100 ? Not to scale ? 350 ? Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the other s base. They cross at a point between them. How high above the ground do they cross? SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 495 ? 540 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 350 ? 360 ? ? ? 110 ? 108 ? Not to scale Not to scale SIC_35 SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 390 ? 414 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 580 ? 550 ? ? ? 117 ? 115 ? Not to scale Not to scale SIC_35 SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 315 ? 360 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 215 ? 455 ? ? ? 126 ? 120 ? Not to scale Not to scale SIC_35 SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 252 ? 270 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 512 ? 256 ? ? ? 140 ? 135 ? Not to scale Not to scale SIC_35 SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 225 ? 240 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 555 ? 452 ? ? ? 150 ? 144 ? Not to scale Not to scale SIC_35 SIC_35
tightly tethered to the others base. They cross at a point between tightly tethered to the other s base. They cross at a point between Two tall vertical masts on horizontal, level ground have guy ropes Two tall vertical masts on horizontal, level ground have guy ropes 190 ? 198 ? them. How high above the ground do they cross? them. How high above the ground do they cross? Strange Guys Strange Guys 533 ? 200 ? ? ? 171 ? 165 ? Not to scale Not to scale SIC_35 SIC_35
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