Assertion (A): If the length of shadow of a person is equal to his height, then the angle of elevation of the sun is 45°.

Statement 2: For any right-angled triangle, tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}}$

1. (A) is true, (R) is false.

2. (A) is false, (R) is true.

3. Both (A) and (R) are true, and (R) is the correct reason for (A).

4. Both (A) and (R) are true, and (R) is the incorrect reason for (A).

Let AB = Height of person and BC = Length of shadow.

∠ACB = θ (Angle of elevation of sun)

Given,

Length of shadow of a person (BC) = height of person (AB)

⇒ tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}}$

⇒ tan θ = $\dfrac{\text{AB}}{\text{BC}}$

⇒ tan θ = $\dfrac{\text{AB}}{\text{AB}}$

⇒ tan θ = 1

⇒ tan θ = tan 45°

⇒ θ = 45°.

∴ Both (A) and (R) are true, and (R) is the correct reason for (A).

Hence, option 3 is the correct option.