Question

A television antenna, which is mounted to the ground, is supported by two cables, extending from the top of the antenna to the ground on opposite sides of the antenna. One cable is 350 meters long and makes a 52-degree angle with the ground. The other cable is 280 meters long. The distance between the cables at the ground in meters?

Answer 1

The distance between the cables at the ground is approximately 195.96 meters.

Step-by-step explanation:

To find the distance between the cables at the ground, we can use trigonometry. Let's call the distance between the cables at the ground 'x'. We can use the sine function to solve for 'x'. Since one cable is 350 meters long and makes a 52-degree angle with the ground, we can write the equation:

sin(52) = x / 350

Solving for 'x', we get:

x = 350 * sin(52)

Next, we need to find the angle between the two cables at the ground. Since we know the lengths of both cables and the distance between them, we can use the Pythagorean theorem. Let's call the angle between the two cables 'θ'. We can write the equation:

x^2 + (280)^2 = 350^2

Solving for 'x', we get:

x = sqrt(350^2 - 280^2)

Thus, the distance between the cables at the ground is approximately 195.96 meters.