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19 February, 21:31

Solve the triangle.

A = 33°, a = 19, b = 14

Select one:

a. B = 23.7°, C = 143.3°, c ≈ 23.3

b. B = 23.7°, C = 123.3°, c ≈ 17.5

c. Cannot be solved

d. B = 23.7°, C = 123.3°, c ≈ 29.2

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Answers (1)
  1. 19 February, 21:51
    0
    Using the sine law to find the value of angle B:

    a / sin A = b / sin B

    19 / sin 33 = 14 / sin B

    B = arcsin (14 * sin 33 / 19)

    B = 23.66° = 23.7°

    Since the sum of all interior angles of a triangle is 180 °, we can solve for angle C like so:

    C = 180 ° - 23.7° - 33 °

    C = 123.3 °

    Using sine law to solve for side c:

    a / sin A = c / sin C

    c = (a*sin C) / sin A

    c = 29.157 = 29.2

    Therefore, among the choices, the correct answer is D.
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