Statement 1: At a particular time, the length of the shadow of a 50 m tower is $50\sqrt{3}$ m.

Statement 2: The sun's altitude is 30°.

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.

In figure,

Let AB be the tower and BC be the shadow.

Join AC.

Given, AB = 50 m and BC = 50 $\sqrt{3}$ m.

As tower is perpendicular to its shadow, thus ΔABC is a right angled triangle,

By formula,

$\Rightarrow \text{tan θ} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{50}{50\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{1}{\sqrt{3}} \\[1em] \Rightarrow \text{tan θ} = \text{tan 30°} \\[1em] \Rightarrow \text{θ} = 30°.$

∴ Both the statements are true.

Hence, option 1 is the correct option.