Armed Forces Classification Test (AFCT) Arithmetic Reasoning Practice Test

If a pole is 3 feet above the ground and its shadow is 4 feet long, how far is the top of the pole from the end of the shadow?

1. 6 feet

2. 7 feet

3. 5 feet

4. 8 feet

The correct answer is: 6 feet

To find the distance from the top of the pole to the end of the shadow, you can envision a right triangle where one leg is the height of the pole and the other leg is the length of the shadow. The height of the pole is 3 feet, and the shadow is 4 feet long. Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, you can establish the following relationship: Let the length of the hypotenuse (the distance from the top of the pole to the end of the shadow) be represented as \( c \). The relationship can then be written as: \[ c^2 = 3^2 + 4^2 \] \[ c^2 = 9 + 16 \] \[ c^2 = 25 \] \[ c = \sqrt{25} \] \[ c = 5 \] This calculation shows that the distance from the top of the pole to the end of the shadow is 5 feet. Therefore, the correct answer highlights the importance of recognizing the right triangle formed by the