SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given right-angled triangle
STEP 2: Determine the trigonometric ratio to use
[tex]\begin{gathered} Given: \\ opposite=9,hypotenuse=c,\theta=45^^{\circ} \\ \\ Since\text{ we have the opposite and hypotenuse, we use:} \\ sin\theta=\frac{opp}{hyp} \end{gathered}[/tex]
STEP 3: Substitute the given values and solve for c
[tex]\begin{gathered} \sin45=\frac{9}{c} \\ By\text{ cross multiplication,} \\ c\times\sin45=9 \\ Divide\text{ both sides by sin 45} \\ \frac{c\times\sin(45)}{sin45}=\frac{9}{sin45} \\ c=12.72792206 \\ c\approx12.73 \end{gathered}[/tex]
Hence, the value of c is approximately 12.73
