The above principles of mathematical modelling lead to the following steps for mathematical modelling Step 1 Identify the physical situation Step 2 Convert the physical situation into a mathematical model by introducing parameters variables and using various known physical laws and symbols Step 3 Find the solution of the mathematical problem Step 4 Interpret the result in terms of the original problem and compare the result with observations or experiments Step 5 If the result is in good agreement then accept the model Otherwise modify the hypotheses assumptions according to the physical situation and to Step 2 The above steps can also be viewed through the following diagram Let Now Physical Introduce Mathematical Situation Model Physical Laws and Symbols or Accept the Model not Modify Hypothesis Not in Good Agreement Fig A 2 1 Example 1 Find the height of a given tower using mathematical modelling Solution Step 1 Given physical situation is to find the height of a given tower Step 2 Let AB be the given tower Fig A 2 2 Let PQ be an observer measuring the height of the tower with his eye at P Let PQ h and let height of tower be H Let a be the angle of elevation from the eye of the observer to the top of the tower Solve Mathematical Interpret Solution In Good Agreement Fig A 2 2 1 Rationalised 2023 24 tan 1 PC QB AC H h PC 1 B Compare with Observation Original Problem H h H MATHEMATICAL MODELLING 199 H h 1 tan a 1 Step 3 Note that the values of the parameters h I and a using sextant are known to