Question

State whether the following statement is true or false. Justify your answer. The value of $\tan A$ is always less than $1$.

• A. True
• B. False

Answer 1

The correct option is B False

Explanation for the statement:

Consider a $∆\mathrm{ABC}$ where $\angle \mathrm{B}=90°,\mathrm{AB}=3,\mathrm{BC}=4\mathrm{and}\mathrm{AC}=5$.

The right-angled triangle can be formed with sides equal to $3$ and $4$ and hypotenuse is $5$ as it will follow the Pythagoras's theorem.

In $∆\mathrm{ABC}$,

$\begin{array}{rcl}{\mathrm{AC}}^2& =& {\mathrm{AB}}^2+{\mathrm{BC}}^2\\ \mathrm{LHS}& =& 5^2\\ & =& 25\\ \mathrm{RHS}& =& 3^2+4^2\\ & =& 9+16\\ & =& 25\\ \therefore \mathrm{LHS}& =& \mathrm{RHS}\end{array}$

Hence, $∆\mathrm{ABC}$ is possible with the considered values.

We have, $\tan A=\frac{4}{3}>1$ i.e., the value of $\tan A$ is greater than $1$.

Hence, the given statement is false.