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Zorluk: KolayTriangles and Pythagorean Theorem

A drone takes off from a launch pad and flies 88 kilometers due north. It then turns and flies 1515 kilometers due east. What is the straight-line distance from the launch pad to the drone's current position?

  1. A
    1313 kilometers
  2. 1717 kilometersCevap
  3. C
    2323 kilometers
  4. D
    6060 kilometers

Cevap

The straight-line distance is 1717 kilometers.
The drone's path forms a right triangle because north and east are perpendicular directions. The straight-line distance between the launch pad and the current position is the hypotenuse. Using the Pythagorean theorem, we calculate 82+152=2898^2 + 15^2 = 289. The square root of 289289 is 1717, making the straight-line distance 1717 kilometers.

Adım Adım Çözüm

1
Identify the shape formed by the drone's flight path.
The path forms a right triangle, with the north and east paths as the legs.
North and east directions are perpendicular to each other, creating a 90∘90^\circ angle.
2
Set up the Pythagorean theorem equation.
a2+b2=c2a^2 + b^2 = c^2, where a=8a = 8 and b=15b = 15.
The straight-line distance from the start to the current position represents the hypotenuse (cc).
3
Square the lengths of the two legs and add them together.
82+152=64+225=2898^2 + 15^2 = 64 + 225 = 289.
This calculates the value of c2c^2 according to the theorem.
4
Find the square root of the sum to determine the hypotenuse.
289=17\sqrt{289} = 17.
Taking the square root of c2c^2 gives the actual straight-line distance.

Anahtar Kavram

The Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) is used to find the hypotenuse of a right triangle when both legs are known.
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Konular

Triangles and Pythagorean Theorem

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