Two guy wires are attached to a cell tower. The first one is 15 ft long and at an angle of elevation on the ground of 55 degrees. The second wire is 22 ft long an angle of elevation on the ground of 63 degrees. Both wires secured same location on ground. How far apart the wires on cell tower?
To find the distance between the two wires on the cell tower, we need to find the horizontal distance covered by each wire.
Let's start with the first wire. The length of the first wire is 15 ft, and the angle of elevation on the ground is 55 degrees. This angle represents the angle between the wire and the ground, and it forms a right triangle with the wire and the ground.
Using trigonometry, we can find the horizontal distance covered by the first wire. We use the cosine function because it relates the adjacent side (horizontal distance) to the hypotenuse (length of the wire).
cos(angle) = adjacent / hypotenuse
cos(55 degrees) = adjacent / 15 ft
To find the adjacent side, we rearrange the equation:
adjacent = cos(55 degrees) * 15 ft
Using a calculator or trigonometric table, we can evaluate the cosine of 55 degrees, which is approximately 0.5736.
adjacent ≈ 0.5736 * 15 ft ≈ 8.604 ft
So, the horizontal distance covered by the first wire is approximately 8.604 ft.
Now, let's move on to the second wire. The length of the second wire is 22 ft, and the angle of elevation on the ground is 63 degrees. We can follow the same process as before:
cos(angle) = adjacent / hypotenuse
cos(63 degrees) = adjacent / 22 ft
To find the adjacent side:
adjacent = cos(63 degrees) * 22 ft
Using a calculator or trigonometric table, we can evaluate the cosine of 63 degrees, which is approximately 0.4481.
adjacent ≈ 0.4481 * 22 ft ≈ 9.857 ft
So, the horizontal distance covered by the second wire is approximately 9.857 ft.
Finally, to find the distance between the two wires on the cell tower, we subtract the horizontal distances covered by each wire:
Distance between wires = distance covered by second wire - distance covered by first wire
Distance between wires ≈ 9.857 ft - 8.604 ft ≈ 1.253 ft
Therefore, the two wires on the cell tower are approximately 1.253 ft apart.
Of course you made a diagram.
let the distance to the first connection be x
let the distance to the second connection by y
x < y
from the smaller right-angled triangle:
sin55 = x/15
x = 15sin55
from the larger triangle:
sin 63 = y/22
y = 22sin63
distance between the two connection points
= y - x
= .......