Question

If $\tan 12=\dfrac{22}{x}$ , then x is equals to,
( a ) 103.5
( b ) 4.7
( c ) 4.6
( d ) 103.6

Answer 1

Hint : Now, firstly we will find the value of tan12 which can be calculated by using a scientific calculator and then we will substitute the value of tan12 in $\tan 12=\dfrac{22}{x}$ . This will give the linear equation which further can be solved to obtain the value of x.

Complete step-by-step answer :
Now , firstly we will find the value of tan12 up to five decimals places. Value of $\tan 12$ can be evaluated using a scientific calculator. We just input the function tanx in along with the value of x = 12, we get value of tan ( 12 ) = 0.21255…. which is approximate value as tan ( 12 ) is non – terminating value
Now, we just simply put the value of tan ( 12 ) = 0.21255 in equation $\tan 12=\dfrac{22}{x}$ to find the value of x.
So, putting value of tan ( 12 ) = 0.21255 in equation, we get
$\tan 12=\dfrac{22}{x}$
$0.21255=\dfrac{22}{x}$
Moving x from denominator on right hand side to numerator of left hand side and 0.21255 from numerator of left hand side to denominator of right hand side using cross multiplication method,
$x=\dfrac{22}{0.21255}$
Multiplying numerator and denominator of right hand side by 100000 we get,
$\begin{aligned} & x=\dfrac{2200000}{21255} \\\ & x=\dfrac{440000}{4251} \\\ & x=103.50505..... \\\ \end{aligned}$
Solving, the equation for x, we get
x = 103.50505….., which is an approximate value up to 5 decimals.
Rounding off the value of x up to 1 decimal we get, x = 103.5
So, the value of x = 103.5.
So, the correct answer is “Option A”.

Note : Calculate the value of tan ( 12 ) in degree only because in radian the value will get changed and the answer will get wrong. As, numerical values are large for calculation so first simplify the larger values in a simpler fraction then solve for an accurate answer.