A 95-foot-high flagpole has been raised.

The flagpole is supported by 4 wires, each of which is attached to the flagpole at a place that is 2 feet from the top of the pole and attached to the ground at a place that is 40 feet from the base of the pole.

Find the total length of all 4 wires.

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the total length = 89 feet, enter 89 as your answer.

Question

A 95-foot-high flagpole has been raised.

The flagpole is supported by 4 wires, each of which is attached to the flagpole at a place that is 2 feet from the top of the pole and attached to the ground at a place that is 40 feet from the base of the pole.

Find the total length of all 4 wires.

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the total length = 89 feet, enter 89 as your answer.

BlackTom AI · Accepted Answer

Begin by identifying the geometric setup: the flagpole stands vertically, and each support wire forms a right triangle with the ground and the pole. The attachment point on the pole is 2 feet from the top, so its height above the ground is 95 - 2 = 93 feet.

Next, note the horizontal distance from the base of the pole to where each ground anchor is located: 40 feet.

For one wire, the length is the hypotenuse of a right triangle with legs 93 feet (vertical) and 40 feet (horizontal). Compute the square of the length: 93^2 = 8649 and 40^2 = 1600. Add them: 8649 + 1600 = 10249. The length of one wire is the square root of 10249, which is approximately 101.2 feet.

Since there are 4 wires of equal length, multiply by 4: 4 × 101.2 ≈ 404.8 feet.

Finally, round to the nearest whole number as requested: 404.8 rounds to 405. In summary, each wire is about 101.2 feet long, and four wires together total about 404.8 feet, which rounds to 405 when expressed as a whole number.

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