A person standing 20 meters away from the base of a tower observes that the angle of elevation to the top of the tower is 60°. Find the height of the tower. (Rounded off to two decimal places)

The correct option is 34.64 m.

Step 1: Identify the given information
Let the height of the tower be $h$ meters.
The distance of the person from the base of the tower ($adjacent\; side$) = $20\text{m}$.
The angle of elevation to the top of the tower ($\theta$) = $60°$.

Step 2: Use the trigonometric ratio for tangent
In a right-angled triangle formed by the person, the base of the tower, and the top of the tower:

$\tan \left(\theta \right)=\frac{\text{Opposite side (Height of tower)}}{\text{Adjacent side (Distance from base)}}$

Substitute the given values into the formula:

$\tan (60°)=\frac{h}{20}$

Step 3: Solve for the height ($h$)
We know that $\tan (60°)=\sqrt{3}\approx 1.732$.

$\sqrt{3}=\frac{h}{20}$

$h=20\times \sqrt{3}$

$h\approx 20\times 1.732=34.64\text{m}$

Thus, the height of the tower is 34.64 m.