In ΔLMN, m = 5.9 cm, n = 8.7 cm and ∠L=163°. Find the length of l, to the nearest 10th of a centimeter.

its 14.4

Answer: side l = 14.5 centimeters (approximately)

Step-by-step Explanation: The triangle LMN has been given such that two sides m equals 5.9 and n equals 8.7. Also line l is not given but angle L equals 163. We shall apply the cosine rule to calculate for side l as the given dimensions satisfy the requirements to apply that formulae. The cosine rule states that;

c^2 = a^ + b^2 - 2abCosC

Using the dimensions given, the formulae can be re-written as,

l^2 = m^2 + n^2 - (2mnCosL)

l^2 = 5.9^2 + 8.7^2 - (2{5.9 x 8.7} CosL)

l^2 = 34.81 + 75.69 - 2 (51.33) x - 0.9563

l^2 = 110.5 + 98.1738

l^2 = 208.6738

Add the square root sign to both sides of the equation

l = 14.4455

Approximately to the nearest tenth of a centimeter, l equals 14.5 centimeters