Mathematics

Question

solve triangle ABC


c = 10, B = 35°, C = 65°

Question options: A = 80°, a = 10, b = 6.3

A = 80°, a = 6.3, b = 10.9

A = 80°, a = 10.9, b = 6.3

A = 80°, a = 73.6, b = 6.3
solve triangle ABC c = 10, B = 35°, C = 65° Question options:  A = 80°, a = 10, b = 6.3 A = 80°, a = 6.3, b = 10.9 A = 80°, a = 10.9, b = 6.3 A = 80°, a = 73.6,

1 Answer

  • That figure obviously doesn't go with this problem.  It doesn't matter; this is triangle ABC labeled the usual way.

    c = 10, B = 35°, C = 65°

    We have two angles and a side.  The third angle is obviously

    A = 180° -  35°- 65°  = 80°

    The remaining sides are given by the Law of Sines,

    [tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

    [tex]a = \dfrac{c \sin A}{\sin C} = \dfrac{10 \sin 80}{\sin 65} = 10.866[/tex]

    [tex]b = \dfrac{c \sin B}{\sin C} = \dfrac{10 \sin 35}{\sin 65} = 6.328[/tex]

    Answer: A=80°, a=10.9, b=6.3, third choice

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