Question

Find the value of x, from $ \tan 27 = \dfrac{x}{{10}} $ .

Answer 1

Hint: If the variables of an equation are expressed in terms of a trigonometric function value, then the equation is said to be a trigonometric equation. In this problem, we have given a trigonometric equation and we have to find the value of x. To simplify the equation for x, we need to know the value of $ \tan 27 $ , we can also find it with the help of trigonometric identities but we cannot get the exact value for $ \tan 27 $ .

Complete step by step solution:
 To solve the equation, we need to find the value of $ \tan 27 $ from the table of natural tangents and the exact value of $ \tan 27 $ from the table is $ 0.5095 $ . Now, we will substitute the value of $ \tan 27 $ in the above equation. On substituting, we get,
 $ \Rightarrow 0.5095 = \dfrac{x}{{10}} $
Now, we will multiply both sides with $ 10 $ , we get,
 $ \Rightarrow 0.5095 \times 10 = \dfrac{x}{{10}} \times 10 $
On further solving we get,
 $ \Rightarrow 5.095 = x $
Hence, the value of x from the given equation is $ 5.095 $ .
So, the correct answer is “ $ 5.095 $ ”.

Note: While finding the value of $ \tan 27 $ from the table of natural tangents, the student must be very careful. In the table of natural tangents, firstly we need to go to the extreme left vertical column, starts from $ 0^\circ $ and ends at $ 90^\circ $ and then we need to go downwards till we reach the angle $ 27^\circ $ and after reaching, we need to move horizontally right to the column headed to $ 0' $ and then we get our value i.e $ 0.5095 $ and then, we have to substitute the value of $ \tan 27 $ in the trigonometric equation to find the value of x.