In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°. Find the length of j, to the nearest centimeter.

Question

In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°. Find the length of j, to the nearest centimeter.

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Acacia 3 years 2021-08-31T08:41:19+00:00 1 Answers 301 views 0

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  1. Doris
    0
    2021-08-31T08:43:09+00:00
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    Given:

    In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°.

    To find:

    The length of j, to the nearest centimeter.

    Solution:

    According to Law of sine,

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

    In ΔHIJ, using law of sine, we get

    \dfrac{j}{\sin J}=\dfrac{h}{\sin H}

    \dfrac{j}{\sin (20^\circ)}=\dfrac{40}{\sin (93^\circ)}}

    j=\dfrac{40\times \sin (20^\circ)}{\sin (93^\circ)}}

    On further simplification, we get

    j=\dfrac{40\times 0.34202}{0.99863}

    j=\dfrac{13.6808}{0.99863}

    j=13.69958

    Approximate the value to the nearest centimeter.

    j\approx 14

    Therefore, the length of j is 14 cm.

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