Let's label the length of the cable as L and the height of the pole as H.
From the problem, we have a right triangle formed by the cable, the pole, and the ground. The length of the cable, the height of the pole, and the distance from the foot of the pole to the point where the cable is affixed form a right triangle.
Using trigonometry, we can set up the following relationships:
1. sin(A) = H / L
2. cos(A) = x / L
From equation 2, we can solve for L:
L = x / cos(A)
Substitute this expression for L into equation 1:
sin(A) = H / (x / cos(A))
sin(A) = H * cos(A) / x
Solve for H:
H = x * sin(A) / cos(A)
H = x * tan(A)
Therefore, the length of the cable L is:
L = x / cos(A)
a cable tied to an electric pole is affixed at a point on the ground x meters away from the foot of the pole to keep it upright if the cable makes an angle A with the ground,find the length of the cable
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