Question

What is a formula I can use to find the measurements of an angle within a triangle ?

Answer 1

Step 1: Problem

Step 2: Concept

Apply trigonometry ratio formula to find the missing angles

Step 3: Method

`\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}`
`\begin{gathered} \text{Question 2} \\ \text{Opposite = 4} \\ \text{Adjacent = 13} \\ \tan \theta\text{ = }\frac{\text{opposite}}{\text{adjacent}} \\ \tan \theta\text{ = }(4)/(13) \\ \tan \theta\text{ = }0.3077 \\ \theta\text{ = }\tan ^(-1)0.3077 \\ \theta\text{ = }17.1 \\ \theta\text{ = }17.1 \end{gathered}`
`\begin{gathered} \text{Question 4} \\ \text{Opposite = 11.9} \\ \text{Adjacent = 10} \\ \tan \theta\text{ = }\frac{adjacent}{\text{hypotenuse}} \\ \tan \theta\text{ = }(10)/(11.9) \\ \tan \theta\text{ = 0.8403} \\ \theta\text{ = }\tan ^(-1)\text{ 0.8403} \\ \theta\text{ = 40.0} \end{gathered}`

Step 4: Final answer

Question 2 = 17.1

Question 4 = 40.0