Respuesta :
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,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
In ΔKLM, using law of sine, we get
[tex]\dfrac{k}{\sin K}=\dfrac{l}{\sin L}[/tex]
[tex]\dfrac{k}{\sin (55^\circ)}=\dfrac{48}{\sin (46^\circ)}[/tex]
[tex]k=\dfrac{48\times \sin (55^\circ)}{\sin (46^\circ)}[/tex]
On further simplification, we get
[tex]k=\dfrac{48\times 0.819152}{0.7193398}[/tex]
[tex]k=\dfrac{39.319296}{0.7193398}[/tex]
[tex]k=54.66025 [/tex]
Approximate the value to the nearest inch.
[tex]k\approx 55 [/tex]
Therefore, the length of k is 55 inch.
The length of k, to the nearest inch is ∠K=55°.
Calculation of the length of K:
Since
In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.
Now here we apply law of sine
[tex]a\div sin\A = b\div sin\ B = c\div sin\c \\\\k\div sin \ k = l\div sin\ L\\\\k\div sin\ 55 = 48\div sin\ 66[/tex]
k = 54.66
k = 55 degrees
hence, The length of k, to the nearest inch is ∠K=55°.
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