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Geometry

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To reach a campsite, a hiker first walks for 2 mi at a bearing N 40 degree E. Then He walks 3 mi due east. What are the magnitude and direction of his hike from his stating point to the campsite? Round the distance to the nearest tenth of a mile and the direction to the nearest degree.

  • Geometry -

    Draw a diagram; it helps keep the trig functions straight.

    Starting from (0,0) a walk of 2 mi at N40°E leaves him at

    x = 2sin40° = 1.29
    y = 2cos40° = 1.53

    Now, a walk 3 mi due east leaves him at

    (4.29,1.53)

    The new bearing is an angle θ with tanθ = 4.29/1.53 = 2.80

    so, the new location is 4.55 mi N70°E

  • Geometry -

    thank you soo much :)

  • Geometry -

    can you show us the diagram and tell the reason why we have to use sin and cos

  • Geometry -

    can you tell us in the diagram which is x and which is y please

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