SOLUTION: One end of 30.4m long cable is attached to the top of a 22m tall vertical pole. The cable is extended as far as possible from the base of the pole and is attached to the ground. 1

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Question 180111: One end of 30.4m long cable is attached to the top of a 22m tall vertical pole. The cable is extended as far as possible from the base of the pole and is attached to the ground.
1. What angle, to the nearest degree, does the cable make with the ground?
2. How high up the pole is the cable a horizontal distance of one meter from the pole?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.)The cable is the hypotenuse of a right triangle (HYP).
The height of the pole is one leg(OPP).
The length from the pole to where the cable touches the ground is the other leg(ADJ).
The angle, A, that the cable makes with the ground has the relation
sin%28A%29=OPP%2FHYP=22%2F30.4=0.7237
A=%0D%0A46.4
Angle A is 46.4 degrees.


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2.) The length of ADJ can be calculated from the Pythagorean theorem,
HYP%5E2=OPP%5E2%2BADJ%5E2
30.4%5E2=22%5E2%2BADJ%5E2
ADJ%5E2=924.16-484=440.16
ADJ=20.98
If I reduce that distance by 1 m, it would be 19.98.
The angle remains the same.
The new adjacent side is now 19.98.
The new opposite side can be calculated using,
tan%28A%29=OPP%2FADJ
tan%2846.4%29=OPP%2F19.98
OPP=19.98%2Atan%2846.4%29
OPP=19.98%2A1.050
OPP=20.98
The cable height 1 meter from the pole would be 20.98m.

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