Question

In the figure given below, $AD=4cm$, $BD=3cm$ and $CB=12cm$, then $cot\theta$ equals

• A. $\frac{3}{4}$
• B. $\frac{5}{12}$
• C. $\frac{4}{3}$
• D. $\frac{12}{5}$

Answer 1

The correct option is D

$\frac{12}{5}$

Solve for the value of $cot\theta$

It is given that $AD=4cm,BD=3cm,CB=12cm$

In $△ABD$ , apply Pythagoras Theorem

$$\begin{gathered} {\left(AB\right)}^2={\left(BD\right)}^2+{\left(AD\right)}^2 \\ {\left(AB\right)}^2=4^2+3^2 \\ AB=\sqrt{25}=5cm \end{gathered}$$

Now in $△ABC$ , apply Pythagoras Theorem

$$\begin{gathered} {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2 \\ {\left(AC\right)}^2=5^2+{12}^2 \\ {\left(AC\right)}^2=169 \\ AC=\sqrt{169}=13 \end{gathered}$$

In $△ABC$ $cot\theta$ can be written as

$$\begin{gathered} cot\theta =\frac{BC}{AB} \\ \Rightarrow cot\theta =\frac{12}{5} \end{gathered}$$

Hence the value of $cot\theta$ is $\frac{12}{5}$ and therefore .option (D) is correct.