Find the missing side or angle. Round to the nearest tenth. A=15° C= 120° b=3 c=[? ] Enter

Question

Find the missing side or angle.
Round to the nearest tenth.
A=15°
C= 120°
b=3
c=[? ]
Enter

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Ladonna 6 months 2021-07-25T05:27:52+00:00 1 Answers 12 views 0

Answers ( )

    0
    2021-07-25T05:29:37+00:00

    Given:

    A=15^\circ, C=120^\circ,b=3.

    To find:

    The length of side c.

    Solution:

    According to the angle sum of property of a triangle, the sum of all interior angles of a triangle is 180 degrees.

    m\angle A+m\angle B+m\angle C=180^\circ

    15^\circ+m\angle B+120^\circ=180^\circ

    m\angle B+135^\circ=180^\circ

    m\angle B=180^\circ-135^\circ

    m\angle B=45^\circ

    According to the Law of sines,

    \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

    Using Law of sines, we get

    \dfrac{b}{\sin B}=\dfrac{c}{\sin C}

    \dfrac{3}{\sin 45^\circ}=\dfrac{c}{\sin 120^\circ}

    \dfrac{3}{\dfrac{1}{\sqrt{2}}}=\dfrac{c}{\dfrac{\sqrt{3}}{2}}

    3\sqrt{2}\times \dfrac{\sqrt{3}}{2}=c

    On further simplification, we get

    \dfrac{3\sqrt{6}}{2}=c

    3.674235=c

    c\approx 3.7

    Therefore, the length of side c is about 3.7 units.

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