(Solved): 5. The cosine rule helps us in calculating one side of a triangle when the angle opposite and the o ...

5. The cosine rule helps us in calculating one side of a triangle when the angle opposite and the other two sides are known. $c^2=a^2+b^2?2ab\cos C$ For the triangle above, assume that $a=5$ and $b=7$, find $a$, given that $C=50^{?}$, find the value of side c. (first write down your steps manually before coding) 6. Write an iPython program (that you can show to your instructor), that will provide a solution to the following scenario. Notice that initially the problem is expressed very haphazardly. Sediment deposited on the north side of a river's mouth increases the beach at a rate of $5\%(0.05)$ in a year. On the south side, the increase is only $2\%(0.02)$ on a yearly basis. At the start of the study period, there is $200\mathrm{cm}$ of sediment on the north side of the river's mouth and $100\mathrm{cm}$ on the south side. The solution needs to calculate and express the amount of the deposition for each side of the river's mouth, and the total amount deposited. The solution's algorithm is expressed below in pseudocode. Normally, you would have developed this algorithm yourself. However, because the purpose of this exercise is for you to get more familiar with Python programming and syntax (also given that we discussed algorithm in class), the algorithm is provided for you in the form of a pseudocode.