The height of a tower is 20 m. The length of its shadow made on the level ground, when the sun's elevation is $60^\circ$, is :

Step 1: Identify the given values and the unknown

We are given the height of the tower and the angle of elevation of the sun. We need to find the length of the shadow cast by the tower. This forms a right-angled triangle where the tower is the perpendicular, the shadow is the base, and the angle of elevation is the angle between the base and the hypotenuse.

Step 2: Choose the appropriate trigonometric ratio

In the right-angled triangle formed, the height of the tower (AB) is opposite to the angle of elevation, and the length of the shadow (BC) is adjacent to the angle of elevation. The tangent function relates the opposite side to the adjacent side.

Step 3: Substitute the values and solve for the unknown

Substitute the given angle of elevation, $60^\circ$, and the height of the tower, $20\text{ m}$, into the tangent equation. We know that $\tan 60^\circ = \sqrt{3}$. Now, we can solve for BC, the length of the shadow.

Step 4: Rationalize the denominator

To present the answer in a standard form, we rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{3}$. This eliminates the radical from the denominator.

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