Respuesta :
We have been given that in ΔLMN, l = 870 cm, ∠N=117° and ∠L=17°. We are asked to find the length of n to the nearest 10th of a centimeter.
We will use law of sines to find the length of n.
Law of sine states the relation between the angles of a triangle and their corresponding side.
[tex]\frac{a}{\text{sin(A)}}=\frac{b}{\text{sin(B)}}=\frac{c}{\text{sin(C)}}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.
Upon using law of sines, we will get:
[tex]\frac{n}{\text{sin(N)}}=\frac{l}{\text{sin(L)}}[/tex]
[tex]\frac{n}{\text{sin}(117^{\circ})}=\frac{870}{\text{sin}(17^{\circ})}[/tex]
[tex]\frac{n}{0.891006524188}=\frac{870}{0.292371704723}[/tex]
[tex]\frac{n}{0.891006524188}\times 0.891006524188=\frac{870}{0.292371704723}\times 0.891006524188[/tex]
[tex]n=2975.66414925226\times 0.891006524188[/tex]
[tex]n=2651.336170776[/tex]
[tex]n\approx 2651.3[/tex]
Therefore, the length of n is approximately 2651.3 cm.
