The ratio of the length of a vertical pole and length of its shadow on the horizontal surface is 3 : $\sqrt{3}$

Assertion(A): The angle of elevation of the sun is 60°.

Reason(R): If angle of elevation of the sun is θ, tan θ = $\dfrac{3}{\sqrt{3}} = \sqrt{3}$ = tan 60°.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

The length of the ladder placed against a vertical wall is twice the distance between the foot of the ladder and the wall.

Assertion(A): The angle that the ladder makes with the wall is 60°.

Reason(R): If ladder makes angle θ with the wall then sin θ = $\dfrac{\text{base}}{\text{hypotenuse}} = \dfrac{x}{2x} = \dfrac{1}{2}$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

CD = 100 m, ∠ADB = 15° and ∠BDC = 45°

Statement (1): AB = $\dfrac{\text{tan 60° - tan 45°}}{100}$

Statement (2): AB = (100 tan 60° - 100 tan 45°) m.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Find AD.

(i)

(ii)