In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°. Find the length of k, to the nearest inch.\

Question

In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°. Find the length of k, to the nearest inch.\

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Ladonna 4 years 2021-08-22T09:09:38+00:00 1 Answers 6 views 0

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  1. ngochoa
    0
    2021-08-22T09:11:35+00:00
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    Given:

    In  ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.

    To find:

    The length of k, to the nearest inch.

    Solution:

    According to Law of sine,

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

    In ΔKLM, using law of sine, we get

    \dfrac{k}{\sin K}=\dfrac{l}{\sin L}

    \dfrac{k}{\sin (55^\circ)}=\dfrac{48}{\sin (46^\circ)}

    k=\dfrac{48\times \sin (55^\circ)}{\sin (46^\circ)}

    On further simplification, we get

    k=\dfrac{48\times 0.819152}{0.7193398}

    k=\dfrac{39.319296}{0.7193398}

    k=54.66025

    Approximate the value to the nearest inch.

    k\approx 55

    Therefore, the length of k is 55 inch.

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