Q&A: An underground sprinkler system is laid at an angle of 34.5 degrees to a fence.?
January 25, 2012
Question by : An underground sprinkler system is laid at an angle of 34.5 degrees to a fence.?
An underground sprinkler system is laid at an angle of 34.5 degrees to a fence. The sprinkler jets are 10m apart and have a range of 12m. Determine the length of the fence that gets wet from the sprinklers, to the nearest tenth of a metre. the answer is 20.5m
I did sin34.5=0.566
1st sprinkler =5.66m away
2nd=11.32m
3rd=16.98m
r=20cos34.5=16.48 i dont know what im doing wrong
Best answer:
Answer by falzoon
Draw triangle ABC with A at the 34.5º vertex, B on the sprinkler at 10m from A,
and C on the fence, 12m from B. Let AC = x.
Then, by the cosine rule, cos(34.5º) = (10^2 + x^2 – 12^2)/(2*10*x)
Rearranging this to quadratic form and solving, gives x = 18.8 to 1 decimal place.
Now move point B to 20m distant from point A and point C may also move.
Now by the cosine rule, cos(34.5º) = (20^2 + x^2 – 12^2)/(2*20*x)
Solving gives x = 20.4.
That didn’t move very much from the previous point C, but we need
to see what happens at the next sprinkler jet.
cos(34.5º) = (30^2 + x^2 – 12^2)/(2*30*x)
Solving this for x gives no real solutions, only imaginary ones,
so it appears that BC, in this situation, must be greater than 12m.
Thus, the answer must be x = 20.4m.
Know better? Leave your own answer in the comments!
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