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Source: various maths texts!
Strange Guys Source: various maths texts!
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Strange Guys 900 π 100 π Not to scale β π 350 π Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross?
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Strange Guys β π₯ = π π and β πβπ₯ = π π π₯= βπ π and πβπ₯= βπ π
From similar triangles: β π₯ = π π and β πβπ₯ = π π Rearranging: π₯= βπ π and πβπ₯= βπ π Adding gives: π= βπ π + βπ π
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Strange Guys π=βπ 1 π + 1 π 1=β π+π ππ So β= ππ π+π Or 1 β = 1 π + 1 π
π₯ π π= βπ π + βπ π π=βπ 1 π + 1 π 1=β π+π ππ So β= ππ π+π Or 1 β = 1 π + 1 π Notice that the distance between the masts is irrelevant to the question asked.
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The guys cross 90 π above the ground.
Strange Guys π π β π For: π=100 π=900 β= (100) =90 The guys cross 90 π above the ground.
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Strange Guys Can you simply explain why the distance π is irrelevant?
β π π π Can you simply explain why the distance π is irrelevant? Imagine the diagram was printed on a rubber sheet and then stretched parallel to the ground.
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Strange Guys Can you simply explain why the distance π is irrelevant?
π π Can you simply explain why the distance π is irrelevant? Imagine the diagram was printed on a rubber sheet and then stretched parallel to the ground. You can see that β is unaltered by the transformation. Note also that the ratio π₯:π¦ is unaltered.
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RESOURCES
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Strange Guys 900 π 100 π Not to scale β π 350 π Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 108 π 540 π 350 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 110 π 495 π 360 π β π Not to scale SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 115 π 414 π 550 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 117 π 390 π 580 π β π Not to scale SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 120 π 360 π 455 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 126 π 315 π 215 π β π Not to scale SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 135 π 270 π 256 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 140 π 252 π 512 π β π Not to scale SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 144 π 240 π 452 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 150 π 225 π 555 π β π Not to scale SIC_35
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Strange Guys Strange Guys β β
Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 165 π 198 π 200 π β π Not to scale SIC_35 Two tall vertical masts on horizontal, level ground have guy ropes tightly tethered to the otherβs base. They cross at a point between them. How high above the ground do they cross? Strange Guys 171 π 190 π 533 π β π Not to scale SIC_35
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