Answer

Verified

349.8k+ views

**Hint:**To find the acute angle $\theta $, we will look for the given value $3.1749$ or less than $3.1749$ in the table. If we are able to get the exact value $3.1749$ in the table, then it will be required to angle $\theta $. If we get the value less than $3.1749$, then we will subtract the obtained value less than $3.1749$ from $3.1749$ and we will look at the difference value in the table of mean difference. After combining this obtained value, we will get the acute angle of $\theta $.

**Complete step by step answer:**

Since, we already have the table of tangents. We will look in the table for the angle that has the value $3.1749$ or less than $3.1749$.

$\Rightarrow \text{Value of}\tan \theta \le 3.1749$

As we know that in the table of tangent that there are not any value of $\theta $ is equal to $3.1749$ but at the row of angle of $72{}^\circ $ and in the column of $30'$, we observe the value of $\theta $ as $3.1716$ that is less than $3.1749$.

$\Rightarrow \text{Value of}\tan 72{}^\circ 30'=3.1716<3.1749$

Now, we will find the difference of $3.1716$ and $3.1749$ as:

$\begin{align}

& =3.1749-3.1716 \\

& =0.0033 \\

\end{align}$

Again, we will see the same row of angle but we will look for the column of mean difference in the table of tangents for the value of $0.0033$. We can find this value in a column of $1'$ of mean difference. So, we will add $1'$ in $72{}^\circ 30'$ to get the required angle as:

$\Rightarrow \text{Value of}\tan \left( 72{}^\circ 30'+1' \right)=3.1749$

After solving this, we will have:

$\Rightarrow \text{Value of}\tan \left( 72{}^\circ 31' \right)=3.1749$

And we already have $\tan \theta =3.1749$ from the question. So, we can write the above step as:

\[\Rightarrow \tan \left( 72{}^\circ 31' \right)=\tan \theta \]

After comparing both sides, we will get the value of $\theta $ as:

$\Rightarrow \theta =72{}^\circ 31'$

Hence, after using the table the acute angle $\theta $ is equal to $72{}^\circ 31'$.

**Note:**we can check the solution by looking for the value of \[\tan \left( 72{}^\circ 31' \right)\] in the table as:

As we have the angle of tangent as $72{}^\circ 31'$, we will observe the nearest value of $72{}^\circ 31'$ in the row of $72{}^\circ $ and we will get the nearest value in the column of $30'$ that is $0.1716$ as:

\[\Rightarrow \tan \left( 72{}^\circ 30' \right)=0.1716\]

Now, the remaining angle is $1'$. So, we will look for that value in the column of the table of mean difference in the row of $72{}^\circ $ and will get the value $0.0033$. Here, we will add it to get the required answer as:

\[\Rightarrow \tan \left( 72{}^\circ 30'+1' \right)=0.1716+0.0033\]

After addition, we will have:

\[\Rightarrow \tan \left( 72{}^\circ 31' \right)=0.1749\]

Since, we got the given value from the question. Hence, the solution is correct.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Establish a relation between electric current and drift class 12 physics CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Copper is not used as potentiometer wire because class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE