In ΔLMN, m = 9.9 cm, n = 3.1 cm and ∠L=109°. Find the length of l, to the nearest 10th of a centimeter. using Law of Cosines (SAS)
To find the length of side l in triangle ΔLMN, we can use the Law of Cosines for the given side-angle-side (SAS) combination.
The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab*cos(C)
where:
c is the side opposite the angle we know (side l)
a and b are the other two sides
C is the angle opposite side c
Plugging in the values we know:
l^2 = m^2 + n^2 - 2mn*cos(L)
l^2 = 9.9^2 + 3.1^2 - 2(9.9)(3.1)*cos(109°)
l^2 = 98.01 + 9.61 - (61.38)
l^2 = 46.24
l ≈ √46.24
l ≈ 6.8
Therefore, the length of side l is approximately 6.8 cm.