In the given figure (each observation is in cm) tan C is :

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

2. $\dfrac{4}{3}$

3. $\dfrac{3}{4}$

4. $\dfrac{4}{5}$

In Δ ABD,

AB² = AD² + BD²

⇒ (26)² = AD² + (10)²

⇒ 676 = AD² + 100

⇒ AD² = 676 - 100

⇒ AD² = 576

⇒ AD = $\sqrt{576}$

⇒ AD = 24 cm

In Δ ADC,

AC² = AD² + DC²

⇒ AC² = (24)² + (32)²

⇒ AC² = 576 + 1,024

⇒ AC² = 1,600

⇒ AC = $\sqrt{1,600}$

⇒ AC = 40 cm

tan $A = \dfrac{Perpendicular}{Base}$

= $\dfrac{24}{32}$

= $\dfrac{3}{4}$

Hence, option 3 is the correct option.