SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given triangle
STEP 2: Write the given measures
[tex]\begin{gathered} Using\text{ angle }\alpha \\ \alpha=40\degree,b=adjacent=30,c=hypotenuse \end{gathered}[/tex]
STEP 3: State the trigonometric ratio to use
Since we have the adjacent and hypotenuse, we use the tan ratio which is stated below:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
By substitution,
[tex]cos40\degree=\frac{30}{c}[/tex]
By simplification, we cross multiply
[tex]\begin{gathered} c\times\cos40\degree=30 \\ c=\frac{30}{\cos40\degree} \\ c=39.16221868 \\ c\approx39.16cm \end{gathered}[/tex]
Hence, the length of c is approximately 39.16cm
