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March 25, 2017

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I have two questions
two forest fire towers, A and B are 20.3km apart. From tower A, the bearing of tower B is 70 degrees. The ranger in each tower observes a fire and radios the bearing from the tower. the bearing from tower A is 25 degrees and from tower B is 345 degrees. How far, to the nearest tenth of a kilometre is the fire from each tower?

the other questions is:
The interior angles of a triangle are 120 degrees, 40 degrees, and 20 degrees. The longest side is 10cm longer than the shortest side. Determine the perimeter of the triangle to the nearest centimetre.

Thanks

  • Grade 11 Math - ,

    Never attempt a question like this without a sketch or diagram.
    I labeled the position of the fire as F
    and by some simple adding/subtracting of angles, I had angle A = 45° and angle B = 95°, thus angle F = 40° , and AB = 20.3

    By sine law:
    AF/sin95 = 20.3/sin40
    AF = 20.3sin95/sin40 = appr31.46 km

    BF/sin45 = 20.3/sin40
    .....

    the second one is quite easy,
    make a sketch of the triangle, place x as the side opposite the 20° angle and (x+10) opposite the 120° angle.

    by sine law :
    x/sin20 = (x+10)/sin120
    xsin120 = xsin20 + 10sin20
    xsin120 - xsin20 = 10sin20
    x(sin120 - sin20) = 10sin20
    x = 10sin20/(sin120-sin20) = appr 6.527

    so the smallest side is 6.527,
    the largest side is 16.527

    Use the sine law once more to find the third side, then add up the 3 sides.

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