To find the length of the wire, we can use trigonometry.
We can see there is a right triangle formed by the wire, the pole, and the ground. The angle between the wire and the ground is 58 degrees.
We can use the sine function because we are given the opposite side (height of the pole) and we are trying to find the hypotenuse (length of the wire).
sin(58 degrees) = height of the pole / length of the wire
sin(58 degrees) = h / L
L = h / sin(58 degrees)
The height of the pole can be found using the Pythagorean theorem:
20^2 + h^2 = L^2
400 + h^2 = L^2
h^2 = L^2 - 400
h = sqrt(L^2 - 400)
Now, substitute the height into the equation for the length of the wire:
L = sqrt(L^2 - 400) / sin(58 degrees)
L = sqrt(L^2 - 400) / sin(58 degrees)
L = sqrt(L^2 - 400) / sin(58 degrees)
L * sin(58 degrees) = sqrt(L^2 - 400)
L^2 * sin^2(58 degrees) = L^2 - 400
L^2 * (1 - sin^2(58 degrees)) = 400
L^2 * cos^2(58 degrees) = 400
L^2 = 400 / cos^2(58 degrees)
L = sqrt(400 / cos^2(58 degrees))
L = sqrt(400) / cos(58 degrees)
L = 20 / cos(58 degrees)
L = 37.7 ft
Therefore, the length of the wire is 37.7 ft.
A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58o with the ground. Find the length of the wire.
A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58o with the ground. Find the length of the wire.
17.0 ft
32.0 ft
37.7 ft
10.6 ft
1 answer