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Zorluk: OrtaPythagorean Theorem Word Problems

A surveyor is mapping a plot of land and launches a drone from a perfectly flat field. The drone ascends vertically to an altitude of 3030 meters. It then travels horizontally in a straight line for 1616 meters to photograph a landmark. What is the direct line-of-sight distance, in meters, from the launch point on the ground to the drone?

Cevap: 34 meters

Cevap

The direct line-of-sight distance is 3434 meters.
The drone's flight path forms a right-angled triangle relative to the starting point. By applying the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we square the vertical distance (302=90030^2 = 900) and the horizontal distance (162=25616^2 = 256). Adding these values yields 11561156. Taking the square root of 11561156 gives the direct line-of-sight distance, which is 3434 meters.

Adım Adım Çözüm

1
Model the drone's flight path as a right-angled triangle.
The vertical ascent forms one leg (a=30a = 30) and the horizontal flight forms the other leg (b=16b = 16). The direct line-of-sight distance is the hypotenuse (cc).
Vertical and horizontal movements are perpendicular, creating a 90∘90^\circ angle.
2
Apply the Pythagorean theorem to calculate the hypotenuse.
a2+b2=c2a^2 + b^2 = c^2 becomes 302+162=c230^2 + 16^2 = c^2.
The Pythagorean theorem relates the lengths of the legs to the length of the hypotenuse in any right triangle.
3
Square the lengths of the two legs and add them together.
900+256=1156900 + 256 = 1156. So, c2=1156c^2 = 1156.
This evaluates the left side of the equation to isolate c2c^2.
4
Take the square root of the sum to find the actual distance.
c=1156=34c = \sqrt{1156} = 34.
Taking the square root of c2c^2 yields the length of the hypotenuse.

Anahtar Kavram

Applying the Pythagorean theorem to find the hypotenuse in a practical right-triangle scenario.
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Pythagorean Theorem Word Problems

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