A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance from the base of the antenna to the down point DOWN hill is 95 feet.Ignore the amount of cable needed to fasten the cable to the antenna or to the tie downs. How much cable is needed? Draw a pic and label.

Question

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance from the base of the antenna to the down point DOWN hill is 95 feet.Ignore the amount of cable needed to fasten the cable to the antenna or to the tie downs. How much cable is needed? Draw a pic and label.

Answer 1

To find the amount of cable needed, we can break the problem into two parts: the horizontal distance and the vertical distance.

First, let's draw a diagram to visualize the problem:

```
/
/
/
/ 100 ft
/-------- A (Antenna)
/
/ 12 degrees
/
/
/------------B (Down point down hill)
```

In the diagram above:
- Point A represents the antenna (100 ft tall).
- Point B represents the down point down the hill.
- The horizontal distance from A to B is 95 ft (given).
- The hill makes an angle of 12 degrees with the horizontal.

Now, let's calculate the horizontal and vertical distances and use them to find the total cable length.

Horizontal Distance:
The horizontal distance can be found using trigonometry. Since we have the angle (12 degrees) and the hypotenuse (distance from A to B, which is 95 ft), we can use the cosine function to find the horizontal distance:

Horizontal distance = Distance AB * cos(angle)

Horizontal distance = 95 ft * cos(12 degrees)

Vertical Distance:
The vertical distance can be found using the sine function. Again, we have the angle (12 degrees) and the hypotenuse (100 ft), so we can use the sine function to find the vertical distance:

Vertical distance = Distance AB * sin(angle)

Vertical distance = 95 ft * sin(12 degrees)

Total Cable Length:
The total cable length is the sum of the horizontal and vertical distances. So, let's calculate it:

Total cable length = Horizontal distance + Vertical distance
= (95 ft * cos(12 degrees)) + (95 ft * sin(12 degrees))

Evaluating this expression will give us the answer, which is the amount of cable needed to anchor the antenna.