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Difficulty: EasyPythagorean Theorem and Special Right Triangles

A vertical flagpole casts a horizontal shadow on the ground. The distance from the top of the flagpole to the tip of the shadow is 2020 feet. If the length of the shadow is 1616 feet, what is the height, in feet, of the flagpole?

  1. 12Answer
  2. B
    16
  3. C
    25.6
  4. D
    36
  5. E
    4

Answer

12
The flagpole, ground, and line from the top of the pole to the tip of the shadow form a right triangle. The diagonal distance of 2020 feet represents the hypotenuse, and the shadow length of 1616 feet represents one of the legs. Using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we set up the equation a2+162=202a^2 + 16^2 = 20^2, which simplifies to a2+256=400a^2 + 256 = 400. Subtracting 256256 from both sides gives a2=144a^2 = 144. Taking the square root of both sides gives the height of the flagpole as 1212 feet.

Step-by-Step Solution

1
Identify the parts of the right triangle formed by the flagpole, ground, and the line from the top of the flagpole to the shadow's tip.
The hypotenuse (cc) is 2020 feet, and one leg (bb) is 1616 feet.
The flagpole is vertical and the ground is horizontal, forming a right angle. The distance from the top of the pole to the tip of the shadow is the diagonal (hypotenuse).
2
Apply the Pythagorean theorem a2+b2=c2a^2 + b^2 = c^2 to find the missing leg (aa).
a2+162=202a^2 + 16^2 = 20^2, which simplifies to a2+256=400a^2 + 256 = 400.
The Pythagorean theorem relates the lengths of the sides of a right triangle.
3
Solve for the unknown height aa by subtracting and taking the square root.
a2=144  ⟹  a=12a^2 = 144 \implies a = 12 feet.
Isolating a2a^2 gives 144144, and taking the square root of 144144 gives the height of the flagpole.

Key Concept

Pythagorean Theorem
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Topics

Pythagorean Theorem and Special Right Triangles

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