Examkin

Soru

Zorluk: OrtaTriangles and Pythagorean Theorem

A drone takes off from a launch pad and flies 6 kilometers6\text{ kilometers} due south. It then turns and flies due west. If the drone's straight-line distance from the launch pad is now exactly 10 kilometers10\text{ kilometers}, how many kilometers did it fly due west?

  1. A
    4
  2. 8Cevap
  3. C
    16
  4. D
    64

Cevap

The drone flew 8 kilometers due west.
The drone's path forms a right triangle with a known leg of 6 km6\text{ km}, an unknown leg xx, and a hypotenuse of 10 km10\text{ km}. Using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we substitute the known values: 62+x2=1026^2 + x^2 = 10^2. This simplifies to 36+x2=10036 + x^2 = 100. Subtracting 3636 from both sides gives x2=64x^2 = 64. Taking the square root of both sides yields x=8x = 8. Therefore, the drone flew 8 kilometers8\text{ kilometers} due west.

Adım Adım Çözüm

1
Identify the geometric shape formed by the drone's flight path.
The flight path forms a right-angled triangle where the southward and westward paths are the legs, and the straight-line distance is the hypotenuse.
The cardinal directions South and West are perpendicular to each other, forming a 90-degree angle.
2
Set up the Pythagorean theorem equation (a2+b2=c2a^2 + b^2 = c^2).
62+b2=1026^2 + b^2 = 10^2
The southward distance is one leg (a=6a = 6), the westward distance is the unknown leg (bb), and the straight-line distance is the hypotenuse (c=10c = 10).
3
Solve the equation for the unknown leg.
36+b2=100→b2=64→b=836 + b^2 = 100 \rightarrow b^2 = 64 \rightarrow b = 8
Squaring the known sides and subtracting gives the square of the unknown leg. Taking the square root gives the final distance.

Anahtar Kavram

Using the Pythagorean theorem to find a missing leg of a right triangle in a real-world navigation scenario.
Tahmini Süre:1m 0s
Bu soruyu puanla

Konular

Triangles and Pythagorean Theorem

Bu konudan daha fazla soru