Option 3 : 22/3

**Given:**

13 sin θ = 5

**Concept used:**

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

**Calculations:**

Using pythagorus theorem,

⇒ 13^{2} = 5^{2} + Base^{2}

⇒ Base = √(169 – 25) = 12

cos θ = 12/13

tan θ = 5/12

⇒ (24 tan θ + 13 cos θ)/(36 tan θ – 13 cos θ)

⇒ [24 × (5/12) + 13 × (12/13)]/[36 × (5/12) – 13 × (12/13)]

⇒ [(2 × 5) + 12]/[(3 × 5) – 12]

⇒ (10 + 12)/(15 – 12)

⇒ 22/3

**∴ The value of (24 tan θ + 13 cos θ)/(36 tan θ – 13 cos θ) is 22/3**