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14 September, 22:48

2. In, is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work. a = 3, c = 19

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  1. 14 September, 23:07
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    Answer: b=18.8; A=9.1°; B=80.9°; and C=90°

    Solution:

    Assuming that the hypothenuse is c=19 and one leg is a=3

    Using the Phythagoras Theorem:

    c^2=a^2+b^2

    Replacing c=19 and a=3 in the equation above:

    19^2=3^2+b^2

    Squaring:

    361=9+b^2

    Solving for b. Isolating b^2: Subtracting 9 both sides of the equation:

    361-9=9+b^2-9

    352=b^2

    b^2=352

    Square root both sides of the equation:

    sqrt (b^2) = sqrt (352)

    b=18.76166303

    Rounding to the nearest tenth:

    b=18.8

    Angles:

    The opposite angle to the hypothenuse c must be a right angle (angle of 90°):

    C=90°

    Using the trigonometric function sine of the angle A:

    sin A = (Opposite side to angle A) / hypothenuse

    sin A=a/c

    Replacing a=3 and c=19 in the equation above:

    sin A=3/19

    Solving for A:

    A = sin^ (-1) (3/19)

    A=sin^ (-1) (0.157894737)

    A=9.084720297°

    Rounding to the nearest tenth:

    A=9.1°

    Using that the acute angles in a right triangle are complementary (must add 90°):

    A+B=90°

    Replacing A=9.1° in the equation above:

    9.1°+B=90°

    Solving for B: Subtracting 9.1° both sides of the equation:

    9.1°+B-9.1°=90°-9.1°

    B=80.9°
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