Armed Forces Classification Test (AFCT) Arithmetic Reasoning Practice Test

A pole is 3 feet tall. If its shadow is 4 feet long, what is the distance from the top of the pole to the end of the shadow?

1. 5 feet

2. 4 feet

3. 6 feet

4. 3.5 feet

The correct answer is: 5 feet

To find the distance from the top of the pole to the end of the shadow, we can visualize the situation as a right triangle. The height of the pole is one leg of the triangle, the length of the shadow is the other leg, and the distance we want to find (from the top of the pole to the tip of the shadow) is the hypotenuse. In this case, the height of the pole is 3 feet, and the length of the shadow is 4 feet. We can use the Pythagorean theorem to calculate the hypotenuse. According to the theorem: \( c^2 = a^2 + b^2 \) where \( c \) is the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. Here, \( a = 3 \) feet and \( b = 4 \) feet. So we can substitute these values into the formula: \( c^2 = 3^2 + 4^2 \) This simplifies to: \( c^2 = 9 + 16 \) \( c^2 = 25 \) Now, taking the square root of both sides gives us: \(