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
