Question

Using trigonometric table, the value of tan${{60}^{\circ }}$ + 1 is approximately equal to,
(a) 2.73
(b) 4.56
(c) 1.68
(d) None of these

Answer 1

Hint: In trigonometry, the angle ${{60}^{\circ }}$ is considered as one of the standard angles for which the value of all the trigonometric functions are known at this angle. For the tan function, the value at the angle ${{60}^{\circ }}$ i.e. tan${{60}^{\circ }}$ = $\sqrt{3}$. Using this, we can solve this question.

Complete step-by-step answer:

Before proceeding with the question, we must know the formula that will be required to solve this question.
In trigonometry, for angle ${{60}^{\circ }}$, the value of all the trigonometric functions is known. For the tan function, the value of $\tan {{60}^{\circ }}=\sqrt{3}$ . . . . . . . . . . . . . . (1)
In this question, we are required to find the value of tan${{60}^{\circ }}$ + 1.
Using equation (1), we have $\tan {{60}^{\circ }}=\sqrt{3}$. Substituting $\tan {{60}^{\circ }}=\sqrt{3}$ in the expression that is given in the question i.e. $\tan {{60}^{\circ }}$ + 1, we get,
$\tan {{60}^{\circ }}$ + 1 = $\sqrt{3}$ + 1
Also, the approximate value of the irrational number $\sqrt{3}$ = 1.73. Substituting $\sqrt{3}$ = 1.73 in the above equation, we get,
$\tan {{60}^{\circ }}$ + 1 = 1.73 + 1
$\Rightarrow$ $\tan {{60}^{\circ }}$ + 1 = 2.73
Hence, the answer is option (a).

Note: There is a possibility that one may commit a mistake while writing the final answer. After generating the value of $\tan {{60}^{\circ }}$, there is a possibility that one may forget to add 1 to this obtained value of $\tan {{60}^{\circ }}$. Since in the question, we are required to find the value of $\tan {{60}^{\circ }}$ + 1, we have to add 1 to $\tan {{60}^{\circ }}$ in order to get the correct answer.