A vertical tower stands on a horizontal plane. From a point on the ground 22 meters away from the base of the tower, the angle of elevation to the top of the tower is 30 degrees. Find the height of the tower.

Step 1: Identify the given information and unknown

We are given the distance from the base of the tower to the observation point, which is 22 meters. The angle of elevation from this point to the top of the tower is 30 degrees. We need to find the height of the tower, which we can denote as $h$. This scenario forms a right-angled triangle.

Step 2: Choose the appropriate trigonometric ratio

In the right-angled triangle, the height of the tower ($h$) is the side opposite to the angle of elevation, and the distance from the base (22 m) is the side adjacent to the angle. The tangent function relates the opposite and adjacent sides to the angle of elevation.

Step 3: Substitute the value of $\tan(30^\circ)$

We know that the value of $\tan(30^\circ)$ is $\frac{1}{\sqrt{3}}$. Substitute this value into the equation to set up the calculation for $h$.

Step 4: Solve for the height of the tower

To find $h$, multiply both sides of the equation by 22. Then, rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$ to get the final height.

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