Question

In figure 1, $AD=3cm,BD=4cm$ and $CB=12cm$, then the value of tan $\theta$ equals

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

Answer 1

The correct option is B $\frac{5}{12}$

$\Rightarrow \tan \theta =\frac{AB}{BC}$

Now, in $△ADB,$

$\Rightarrow A{B}^2=B{D}^2+A{D}^2$

$=4^2+3^2$

$=25$

$\Rightarrow AB=5cm$

$\therefore \tan \theta =\frac{5}{12}$

Hence, the answer is $\frac{5}{12}.$