The value of tan A is :

1. $\dfrac{5}{12}$

2. $\dfrac{12}{13}$

3. $\dfrac{5}{13}$

4. $\dfrac{13}{12}$

Since ΔPQR is a right angled triangle, using pythagoras theorem,

⇒ Hypotenuse² = Base² + Height²

⇒ PQ² = QR² + PR²

⇒ 13² = PR² + 12²

⇒ 169 = PR² + 144

⇒ PR² = 169 - 144

⇒ PR² = 25

⇒ PR = $\sqrt{25}$

⇒ PR = 5 cm.

By formula, tan A = $\dfrac{\text{Height}}{\text{Base}}$

From figure,

$\text{tan A} = \dfrac{PR}{RQ} \\[1em] = \dfrac{5}{12}.$

Hence, option 1 is the correct option.