Step 1: Problem
Step 2: Concept
Apply trigonometry ratio formula to find the missing angles
Step 3: Method
[tex]\begin{gathered} \text{Given data} \\ \\ \text{Side AB facing right angle C is the hypotenuse } \\ \text{Side BC facing the given angle }\theta\text{ is the opposite} \\ \text{The third side AC is the adjacent} \end{gathered}[/tex][tex]\begin{gathered} \text{Question 2} \\ \text{Opposite = 4} \\ \text{Adjacent = 13} \\ \tan \theta\text{ = }\frac{\text{opposite}}{\text{adjacent}} \\ \tan \theta\text{ = }\frac{4}{13} \\ \tan \theta\text{ = }0.3077 \\ \theta\text{ = }\tan ^{-1}0.3077 \\ \theta\text{ = }17.1 \\ \theta\text{ = }17.1 \end{gathered}[/tex][tex]\begin{gathered} \text{Question 4} \\ \text{Opposite = 11.9} \\ \text{Adjacent = 10} \\ \tan \theta\text{ = }\frac{adjacent}{\text{hypotenuse}} \\ \tan \theta\text{ = }\frac{10}{11.9} \\ \tan \theta\text{ = 0.8403} \\ \theta\text{ = }\tan ^{-1}\text{ 0.8403} \\ \theta\text{ = 40.0} \end{gathered}[/tex]Step 4: Final answer
Question 2 = 17.1
Question 4 = 40.0
