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Zorluk: OrtaPythagorean Theorem and Special Right Triangles

A delivery drone departs from a central launch pad and travels due north for 1212 miles, then turns and travels due east for 1616 miles to reach Drop Point P. A secondary relay station is located 1818 miles due south of the central launch pad. What is the straight-line distance, in miles, from Drop Point P to the secondary relay station?

  1. A
    2020
  2. B
    2828
  3. C
    3030
  4. 3434Cevap
  5. E
    4646

Cevap

The straight-line distance from Drop Point P to the secondary relay station is 3434 miles.
To find the straight-line distance from Drop Point P to the secondary relay station, model the displacement as a right triangle. The horizontal distance is 1616 miles (east). The vertical distance is the sum of 1212 miles north and 1818 miles south, giving 3030 miles. Using the Pythagorean Theorem, d=162+302=256+900=1156=34d = \sqrt{16^2 + 30^2} = \sqrt{256 + 900} = \sqrt{1156} = 34 miles.

Adım Adım Çözüm

1
Set up a coordinate grid relative to the central launch pad.
Central launch pad is at (0,0)(0, 0). Drop Point P is at (16,12)(16, 12). Secondary relay station is at (0,−18)(0, -18).
Establishing coordinates converts the movement into horizontal and vertical components.
2
Calculate the horizontal and vertical distances between Drop Point P and the secondary relay station.
Horizontal distance = ∣16−0∣=16|16 - 0| = 16 miles. Vertical distance = ∣12−(−18)∣=12+18=30|12 - (-18)| = 12 + 18 = 30 miles.
These distances represent the two perpendicular legs of a right triangle.
3
Apply the Pythagorean Theorem to find the hypotenuse.
Distance =sqrt162+302=sqrt256+900=sqrt1156=34= \\sqrt{16^2 + 30^2} = \\sqrt{256 + 900} = \\sqrt{1156} = 34 miles.
The straight-line distance is the hypotenuse of the right triangle formed by the horizontal and vertical legs.

Anahtar Kavram

Pythagorean Theorem for distance in perpendicular directions
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Konular

Pythagorean Theorem and Special Right Triangles

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