Question

How do you solve it \[\tan \theta = \dfrac{5}{9}\] ?

Answer 1

Hint: We need to know the basic formula for \[\tan \theta \] the involvement of the opposite side and adjacent side to solve the given problem. First, we need to find the value of \[\theta \] . The given question involves the operation of addition/ subtraction/ multiplication/ division. Also, we need to know how to calculate the value \[{\tan ^{ - 1}}\] in the calculator. While calculating \[{\tan ^{ - 1}}\] the value we need to know which mode to be selected in the calculator.

Complete step-by-step answer:
The given question is shown below,
 \[\tan \theta = \dfrac{5}{9}\] ?
We need to find the value \[\theta \] in the above equation. Before that, we need to know the basic definition of \[\tan \theta \]

From the figure, we get that,
 \[\tan \theta = \dfrac{{opposite}}{{adjacent}}\] \[ \to \left( 1 \right)\]
The given equation in the question is,
 \[\tan \theta = \dfrac{5}{9}\] \[ \to \left( 2 \right)\]
By comparing the above two equations we get which is the value of the opposite side and which is the value of the adjacent side.
When the term \[\tan \] is moved from the left side to the right side of the equation, it converts into \[{\tan ^{ - 1}}\] . So, we get
 \[\tan \theta = \dfrac{5}{9}\]
 \[\theta = {\tan ^{ - 1}}\left( {\dfrac{5}{9}} \right) \to \left( 3 \right)\]
Let’s simplify the fractional term present in the above equation,
 \[\dfrac{5}{9} = 0.556 \to \left( 4 \right)\]
Let’s substitute the equation \[(4)\] in the equation \[(3)\] , we get
 \[\theta = {\tan ^{ - 1}}\left( {0.556} \right)\]
By calculating \[{\tan ^{ - 1}}\left( {0.556} \right)\] in the calculator in degree mode we get,
 \[\theta = 29.07\]
So, the correct answer is “ \[\theta = 29.07\] ”.

Note: After confirming that, we would find the value of \[\theta \] in the given question. On finding the \[\theta \] value we can use either radian mode or degree mode. If we want to find the value \[\theta \] in decimal value, we can use radian mode in the calculator. If we want to find the value of \[\theta \] in degrees, we can use degree mode in the calculator. Also, note that when” \[\tan \] ” is the move from the left side to the right side of the equation it converts into \[{\tan ^{ - 1}}\] .