Question

Solve the value of B, from $ \sin B = 0.7245 $ .

Answer 1

Hint: If in an equation, the variables are expressed in terms of a trigonometric function value, then it is said to be a trigonometric equation. In this problem, we have given a trigonometric equation and we have to find the value of B. To solve the equation for B, we need to simplify the equation.

Complete step by step solution:
he trigonometric equation given in this problem is,
  $ \sin B = 0.7245 $
To find the value of B we need to divide the equation with $ \sin $ on both sides and after simplifying the above equation, we get,
  $ \Rightarrow B = {\sin ^{ - 1}}\left( {0.7245} \right) $
When the trigonometric function of an angle, comes from one side to other, it got inverse and now, we have to find the value of \[{\sin ^{ - 1}}\left( {0.7245} \right)\]from the log book. In the log book we have to open the natural sines page and from there we get the value of \[{\sin ^{ - 1}}\left( {0.7245} \right)\]i.e, $ 46.43^\circ $ . Hence, the value of B is $ 46.43^\circ $ .
So, the correct answer is “ $ 46.43^\circ $ ”.

Note: In this problem, we need a log book to find the inverse of sin $ 0.7245 $ in the natural sines table. In the table, we have to search for the value $ 0.7245 $ , we may not get the exact value but we can get the nearer value. We have to search the value along the rows and columns and then, we need to find the difference between the values and then, we have to look into the mean difference column along the same row and hence, we will find the value of B for the trigonometric equation.