Part a: Roy sweeps out 2.15/0.7 radians.
Part b: When Roy stops skiing, he is cos(3.071)(0.7) km to the center of the ski trial
Part c: When Roy stops skiing he is sin(3.071)(0.7) km above the centre of the ski trail
The radius of the ski trail= 0.7 km
Roy starts 3 o'clock position and travels 2.15 km in the counter-clockwise direction.
Let O be the centre of ski trial, A be the starting point(3-o'clock position) and consider he is now at point B.
Now, using the formula for arc length.
Arc length=(Radius)(angle at center)
2.15=(0.7)θ
θ=2.15/0.7
Roy sweep out 2.15/0.7 radians.
Part b:
When Roy stops skiing how many km is Roy to the right of the ski trial
In part, a figure draws the vertical line from point B on the horizontal line. Get the right-angle triangle
Here to find the length OP. In right angle triangle cos θ=Adjacent side/hypotenuse,
As in part, a central angle is 2.15/0.7=3.071.
Therefore,
cos(3.071)=OP/0.7
OP=cos(3.071)(0.7)
cos(3.071)(0.7) km.
Part c:
When Roy stops skiing how many km is Roy above the centre of the ski trial
From figure part of part b, we have to calculate side BP.
In right angle triangle sin(θ)=Opposite side/hypotenuse
Therefore,
sin(3.071)=BP/0.7
BP=sin(3.071)/(0.7)
sin(3.071)(0.7) km.
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