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))}`

`(n)/(0.891006524188)=(870)/(0.292371704723)`

`(n)/(0.891006524188)* 0.891006524188=(870)/(0.292371704723)* 0.891006524188`

`n=2975.66414925226* 0.891006524188`

`n=2651.336170776`

`n\approx 2651.3`

Therefore, the length of n is approximately 2651.3 cm.