A 5 metre tall vertical pole is supported by a guy wire. The wire is attached to the top of the pole and is attached to the ground 3 metres from the base of the pole
a^2 + b^2 = c^2. c = Length of wire.
3^2 + 5^2 = c^2.
To solve this problem, we can use the concept of right triangles and the Pythagorean theorem.
Let's label the height of the pole as "h" and the distance from the base of the pole to the attachment point on the ground as "d." We know that the pole is 5 meters tall, so h = 5 meters. We also know that the attachment point on the ground is 3 meters away from the base of the pole, so d = 3 meters.
To find the length of the guy wire, we can use 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.
In this case, the guy wire is the hypotenuse of a right triangle, with the vertical height of the pole as one side and the distance from the base to the attachment point as the other side. So, we can write the equation:
h² + d² = guy wire length²
Substituting the known values, we have:
5² + 3² = guy wire length²
25 + 9 = guy wire length²
34 = guy wire length²
To solve for the guy wire length, we can take the square root of both sides:
√34 = guy wire length
So, the length of the guy wire is approximately 5.83 meters.