A radio antenna 30 m tall standing on a 10 degrees incline is to be braced by two cable extending from the top of the pole to points on the ground 40 m up the slope and 40 m down the slope. how long must the cables be? give the answer to three significant digits.
What I want:
1) A Graph Of That Shape
2) The answer
3) Explanation
What I want:
1) A Graph Of That Shape
2) The answer
3) Explanation
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For the upper cable: the angle the antenna makes with the ground upslope is
90 - 10 = 80 degrees. This will be angle C to side c, the length of the cable,
with a = 30 and b = 40. So using the cosine law we get
c^2 = a^2 + b^2 - 2ab*cos(C) = 30^2 + 40^2 - 2*30*40*cos(80) = 2083.244,
and so cable length c = 45.64 m.
For the lower cable, the only difference is that C = 90 + 10 = 100 degrees, so
c^2 = 30^2 + 40^2 - 2*30*40*cos(100) = 2916.756, and so c = 54.01 m.
90 - 10 = 80 degrees. This will be angle C to side c, the length of the cable,
with a = 30 and b = 40. So using the cosine law we get
c^2 = a^2 + b^2 - 2ab*cos(C) = 30^2 + 40^2 - 2*30*40*cos(80) = 2083.244,
and so cable length c = 45.64 m.
For the lower cable, the only difference is that C = 90 + 10 = 100 degrees, so
c^2 = 30^2 + 40^2 - 2*30*40*cos(100) = 2916.756, and so c = 54.01 m.