Question

Find angle k and angle f I would like to know these two problems please

Answer 1

The given parts in the question are

`\begin{gathered} \text{opposite}=6 \\ \text{adjacent}=5 \\ \text{angle}=k \end{gathered}`

To calculate the value of angle k, we will use the trigonometric ratio

SOH ,CAH, TOA

`\begin{gathered} \sin \theta=(opposite)/(hypotenus) \\ \cos \theta=(adjacent)/(hypotenus) \end{gathered}`

`\begin{gathered} \text{Tan}\theta=(opposite)/(adjacent) \\ \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \text{Tan}\theta=(opposite)/(adjacent) \\ \tan \text{ k =}(6)/(5) \\ \tan \text{ k = 1.2} \end{gathered}`

To find the value of k, we will calculate the value of the arc tan of 1.2 using a calculator or a tangent table

`\begin{gathered} \tan \text{ k = 1.2} \\ k=\tan ^(-1)1.2 \\ k=50.19^0 \\ k\approx50^0 \end{gathered}`

Hence,

The value of angle k = 50° (50 degrees)