Assertion (A): CD = 3 x AB = 3 x 10 m = 30 m

Reason (R): In △ABC, tan30° = $\dfrac{10\text{m}}{\text{BC}}$
⇒ BC = 10 $\sqrt{3}$ m
tan 30° = $\dfrac{10\sqrt{3}\text{m}}{\text{CD}}$
⇒ CD = 30 m

1. A is true, R is false.
2. A is false, R is true.
3. Both A and R are true.
4. Both A and R are false.

Both A and R are true.

Explanation

tan θ = $\dfrac{Perpendicular}{Base}$

In Δ ABC,

tan 30° = $\dfrac{AB}{BC}$

$⇒ \dfrac{1}{\sqrt3} = \dfrac{10}{BC}\\[1em] ⇒ BC = 10\sqrt3 m$

In Δ BCD,

tan 30° = $\dfrac{BC}{CD}$

$⇒ \dfrac{1}{\sqrt3} = \dfrac{10\sqrt3}{CD}\\[1em] ⇒ CD = 10\sqrt3 \times \sqrt3\\[1em] ⇒ CD = 10 \times 3\\[1em] ⇒ CD = 30 m$

According to Assertion, CD = 3 x AB = 3 x 10 m = 30 m

∴ Assertion (A) is true.

From above calculation, in △ABC,

tan30° = $\dfrac{10\text{m}}{\text{BC}}$

⇒ BC = 10 $\sqrt{3}$ m

tan 30° = $\dfrac{10\sqrt{3}\text{m}}{\text{CD}}$

⇒ CD = 30 m

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.