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16 September, 02:29

In the triangle, bc=12 cm and tan c = 0.583. what is the length of the hypotenuse, to the nearest tenth of a centimeter

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Answers (2)
  1. 16 September, 02:36
    0
    We have the following trigonometric relationship:

    tan c = AB / BC

    We cleared AB:

    AB = BC * tan c

    Substituting values:

    AB = (12) * (0.583)

    AB = 6,996

    We now look for the hypotenuse using the Pythagorean theorem:

    hypotenuse = root ((AB) ^ 2 + (BC) ^ 2)

    Substituting values:

    hypotenuse = root ((6,996) ^ 2 + (12) ^ 2)

    hypotenuse = 13.9 cm

    Answer:

    The length of the hypotenuse, to the nearest tenth of a centimeter is:

    hypotenuse = 13.9 cm
  2. 16 September, 02:55
    0
    Given that BC=12 cm and tan C=0.583, the value of the hypotenuse will be given as follows:

    BC is the adjacent, the height AB will be given by

    AB/BC=tan C

    thus

    AB/12=0.583

    AB=12*0.583

    AB=6.996

    hence using Pythagorean theorem:

    c^2=b^2+a^2

    thus;

    c^2=6.996^2+12^2

    c^2=192.944016

    c=13.890~14 cm (to the nearest centimeter)
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