Solution
Step 1
Write an expression for cosine and sine, using their ratios
[tex]\begin{gathered} Co\sin e\text{ =}\frac{adjacent}{\text{hypothenuse}} \\ \sin e\text{ = }\frac{opposite\text{ }}{\text{hypothenuse}} \end{gathered}[/tex]Step 2
Define the values of adjacent, opposite, hypothenuse
From the question Cos(c) = 7/25
Hence by comparison with the ratio above
adjacent = 7
hypothenuse = 25
Opposite =?
Step 3
Find the value of the opposite using Pythagoras theorem
Hence, from the diagram using Pythagoras theorem
[tex]\begin{gathered} \text{hypothenuse}^2=adjacent^2+opposite^2 \\ \text{opposite}^2=hypothenuse^2-adjacent^2 \\ \text{opposite =}\sqrt[]{hypothenuse^2-adjacent^2} \\ After,\text{ substitution} \\ \text{opposite =}\sqrt[]{25^2-7^2} \\ \text{opposite = }\sqrt[]{576} \\ \text{opposite =24} \end{gathered}[/tex]Step 4
Find the value of sine(c)
[tex]\begin{gathered} \text{From the equation above} \\ \sin (c)\text{ = }\frac{opposite}{\text{hypothenuse}},\text{ after susbstitution} \\ \sin (c)\text{ = }\frac{24}{25} \end{gathered}[/tex]Hence, sin(c) = 24/25... Option C
