Question

Two 25-foot strings are tied to the top of a light pole and staked to the ground. The distance

between the stakes is 30 feet. How tall is the pole? (Hint: The pole is halfway between the
stakes.)

Answer 1

The height of the light pole is found using the Pythagorean theorem. The pole forms the vertical side of two right triangles with the 25-foot strings as hypotenuses and half of the 30-foot distance between stakes as the base. The height of the pole is 20 feet.

Step-by-step explanation:

The question asks to determine the height of a light pole that has two 25-foot strings tied to its top and staked to the ground, with the stakes being 30 feet apart. The pole is situated halfway between the stakes, forming two right triangles. To find the height of the pole, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Given that the strings are the hypotenuses of the triangles and they each measure 25 feet, and the distance between the stakes is 30 feet, we can use the Pythagorean theorem:

1. c2 = a2 + b2
2. 252 = b2 + (30/2)2
3. 625 = b2 + 225
4. b2 = 625 - 225
5. b2 = 400
6. b = √400
7. b = 20

So the height of the pole, represented by b, is 20 feet.