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December 2, 2009

national park origin

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Mathematics question.. please help need to be done quick please?

The state government is considering options for constructing a road system which will provide access to a national park and to the nearby town of Jaffra.

The park is triangular in shape. One of the boundary lines is formed by a river which flows from its source, located at the origin O(0,0)to it’s endpoint E with co-ordinates (100,80).

The second boundary line is a fence which has been erected from the point E (100,80) to intersect the x-asis at the point Z with co-ordinates (260,0).

The third boundary is the section of the x-asis between O90,0) and Z(260,0).

The town of Jaffra is located at the point J with Co-ordinates (40,100).

1- Find the equation which represents the river’s path.
2-Find, correct to one decimal place, the magnitude of the angle that the river makes with the positive x-axis.

Please help, and provide working out. Thank you very much :)

1- Let the river’s path be y=mx+b.
Since it passes (100,80) and the origin,
y=80/100x+0
therefore, y=4/5x.
2- Um… I got 45.7° , im not toooo sure.
Let the magnitude of the angle that the river makes with the positive x-axis be θ.
So, tanθ=80/100
θ=4/tan 5
θ=45.7°
…….=D

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