Question

If \[\sqrt 3 = 1.732\], find the value of the following term (correct to two decimal places): and verify whether \[\dfrac{2}{{\tan {{30}^ \circ }}}\] is \[3.46\].

If true enter \[1\] and if false then enter\[0\].

Answer 1

Hint: When it is asked to find up to certain decimal places say \[n\]. So, we take answers up to \[n + 1\] th decimal places. If the \[n + 1\] th decimal place is greater than and equals 5, we will add 1 to the digit of \[n\] th decimal place. If the \[n + 1\] th decimal place is less than 5, there will be no change in the \[n\] th decimal digit.
Value of tangent degree:
$\tan ({0^ \circ }) = 0$
$\tan ({30^ \circ }) = \dfrac{1}{{\sqrt 3 }}$
$\tan ({45^ \circ }) = 1$
$\tan ({60^ \circ }) = \sqrt 3 $
$\tan ({90^ \circ }) = \infty $

Complete step by step answer:
It is given that,
\[\sqrt 3 = 1.732\]
We have to find the value of \[\dfrac{2}{{\tan {{30}^ \circ }}}\] up to correct two decimal places.
Already we know that the value of, \[\tan ({30^ \circ })\],
Therefore we have substitute the value into the given is \[\dfrac{2}{{\tan {{30}^ \circ }}}\] get the required answer,
\[\dfrac{2}{{\tan {{30}^ \circ }}} = \dfrac{2}{{\dfrac{1}{{\sqrt 3 }}}}\]
              \[ = 2\sqrt 3 \]
Substitute the value of \[\sqrt 3 = 1.732\] in the above equation then we get,
\[\dfrac{2}{{\tan {{30}^ \circ }}} = 2 \times 1.732\]
On multiplying the above answer we get,
\[\dfrac{2}{{\tan {{30}^ \circ }}}\]\[ = 3.464\]
Now the question is asked to find up to two decimal places. So, we take the answer up to three decimal places. If the third decimal place is greater than and equals 5, we will add 1 to the digit of the second decimal place. If the third decimal place is less than 5, there will be no change in the second decimal digit.
Here, the digit at the three decimal places is \[4\] which is less than \[5\], so the digit in the second decimal place will be unchanged.
Hence, the value of \[\dfrac{2}{{\tan {{30}^ \circ }}} = 3.46\] (correct up to two decimal place)

Since the given statement is true we will enter 1.

Note:
Correct up to a certain decimal place means simpler form of the answer but it should be closer to the actual answer.