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Difficulty: EasyTriangles and Pythagorean Theorem

A guy wire is anchored to the flat ground and attached to a vertical pole, forming a right triangle. The wire is 1010 meters long and attaches to the pole exactly 88 meters above the ground. What is the horizontal distance from the base of the pole to the anchor point on the ground, in meters?

  1. 66Answer
  2. B
    22
  3. C
    1818
  4. D
    164\sqrt{164}

Answer

The correct answer is 66.
The scenario describes a right triangle where the hypotenuse is 1010 and one leg is 88. Applying the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), we find the unknown leg distance is 102−82=100−64=36=6\sqrt{10^2 - 8^2} = \sqrt{100 - 64} = \sqrt{36} = 6.

Step-by-Step Solution

1
Identify the known sides of the right triangle.
The hypotenuse (the wire) is 1010 meters, and one vertical leg (the height on the pole) is 88 meters.
Assigning the correct values to the Pythagorean theorem formula ensures the proper calculation path.
2
Set up the Pythagorean theorem equation.
x2+82=102x^2 + 8^2 = 10^2, where xx is the unknown horizontal distance.
The Pythagorean theorem relates the lengths of the legs to the hypotenuse in a right triangle.
3
Square the known values and solve for x2x^2.
x2+64=100x^2 + 64 = 100, which simplifies to x2=100−64=36x^2 = 100 - 64 = 36.
Isolating the squared variable term is necessary to find the missing side length.
4
Take the square root to find the final distance.
x=36=6x = \sqrt{36} = 6.
Taking the square root converts the squared area value back into a linear distance.

Key Concept

The Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) allows you to find a missing leg of a right triangle when the hypotenuse and the other leg are known.
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Topics

Triangles and Pythagorean Theorem

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