To find the length of the wire structure from the top of one pole to the top of the other pole, we can use the Pythagorean theorem since the wire forms the hypotenuse of a right triangle.
Let's denote:
- \( h_1 \) as the height of the first pole (15 m)
- \( h_2 \) as the height of the second pole (7.5 m)
- \( d \) as the distance between the two poles (18 m)
- \( l \) as the length of the wire structure we want to find
According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle (the heights of the poles in this case) is equal to the square of the length of the hypotenuse (the length of the wire structure). Therefore, we can write:
\[ l^2 = h_1^2 + d^2 \]
Substituting the given values:
\[ l^2 = (15)^2 + (18)^2 \]
\[ l^2 = 225 + 324 \]
\[ l^2 = 549 \]
Now, we take the square root of both sides to find \( l \):
\[ l = \sqrt{549} \]
\[ l \approx 23.43 \, \text{meters} \]
Therefore, the length of the wire structure from the top of one pole to the top of the other pole is approximately 23.43 meters.Answer:
Step-by-step explanation:
