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21 December, 05:02

The radar operator at an airport control tower locates two planes flying toward the airport at the same altitude. One plane is 120km away from the airport at a bearing of North 70 degree East. The other is 180km away, on a bearing of South 55 degree East. How far apart are the planes?

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  1. 21 December, 05:13
    0
    In order to answer this question, we find first the x and y components of the distances given.

    1st plane:

    x-component: x = (120 km) (sin 70°) = 112.76 km

    y-component: y = (120 km) (cos 70°) = 41.04 km

    2nd plane:

    x-component: x = (180 km) (sin 55°) = 147.45 km

    y-component: y = (180 km) (cos 55°) = - 103.24 km (negative because it is in the south)

    The distance between these planes is calculated through the equation

    d = √ (x₂ - x₁) ² + (y₂ - y₁) ²

    Substituting the calculated values

    d = √ (112.76 - 147.45) ² + (41.04 - (-103.24)) ²

    d = 148.39 km

    Thus, the distance between these planes is approximately 148.39 km
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