Question

In ΔLMN, l = 870 cm, ∠N=117° and ∠L=17°. Find the length of n, to the nearest 10th of a centimeter.

Answer 1

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.

$\frac{a}{\text{sin(A)}}=\frac{b}{\text{sin(B)}}=\frac{c}{\text{sin(C)}}$, where a, b and c are corresponding sides to angles A, B and C respectively.

Upon using law of sines, we will get:

$\frac{n}{\text{sin(N)}}=\frac{l}{\text{sin(L)}}$

$\frac{n}{\text{sin}(117^{\circ})}=\frac{870}{\text{sin}(17^{\circ})}$

$\frac{n}{0.891006524188}=\frac{870}{0.292371704723}$

$\frac{n}{0.891006524188}\times 0.891006524188=\frac{870}{0.292371704723}\times 0.891006524188$

$n=2975.66414925226\times 0.891006524188$

$n=2651.336170776$

$n\approx 2651.3$

Therefore, the length of n is approximately 2651.3 cm.