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TRIGONOMETRY HELP PLEASE?

An airplane travels at 180 ​km/hr for 2 hours in a direction of 210degrees. At the end of this​ time, how far south of the airport is the​ airplane?

Note: Directions are given in degrees clockwise from north.

The airplane is ____ kilometers south of the airport after 2 hours?

3 Answers

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  • 2 months ago

    210º is 30º S of N

    180 km/hr x 2 hr = 360 km

    d = 360 sin 30 = 360/2 = 180 km

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  • DWRead
    Lv 7
    2 months ago

    2 hours × (180 km)/hour = 360 km

    Draw a picture. The path of the airplane is the hypotenuse of a 30-60-90 triangle. The sides of a 30-60-90 triangle are in the ratio 1:√3:2.

    The hypotenuse is 360 km, so the side opposite the 60° angle is 180√3 km ≅ 312 km.

    The airplane is 312 km south of the airport.

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  • 2 months ago

    Make a drawing (it does not have to be to scale - but it will help you understand). Make it look like an x-y plot (Cartesian grid). Leave more room below than above (the airplane is moving "down" on your graph).

    At the origin (0, 0), put the airport.

    Label the axes:

    The positive (right) end of the x axis is 090 degrees (East)

    The negative (bottom) end of the y axis is 180 degrees (South)

    The negative (left) end of the x axis is 270 degrees (West)

    The positive (top) end of the y axis is 360 degrees (in marine navigation, we use 000, but it means the same thing: due North)

    210 is the direction that is 30 degrees "clockwise" from due South (180)

    Draw a line in that direction.

    The length of the line is 2 h times 180 km/h = 360 km

    This length will become the hypotenuse of the triangle we will construct:

    From the end of this line, draw a horizontal line that will hit the y-axis at a 90-degree angle. You now have a right-angle triangle formed by the hypotenuse, the y-axis and this perpendicular line you just added.

    You are looking for the length along the y-axis (it is the north-south line - therefore it is on that line that you measure how far south you are).

    It is adjacent to the angle (at the centre origin).

    adjacent/hypotenuse = cosine

    adjacent = cosine * hypotenuse = cos(210) * 360

    If you do this directly on a calculator, you will see that the machine will automatically give you a negative value (cosine of 210 is a negative value). This will give you a negative value for the length of the adjacent side; when doing navigation problems in that fashion, a negative value for y means south.

    I get a "southing" of around 312 km. I suggest that you write down the more precise value that you will get when you do it yourself.

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