STEP-BY-STEP DERIVATION 1 Identify the given information and unknown. Distance from tower base $= 18 \text{ m}$ Angle of elevation $= 30^\circ$ Height of tower $= h = ?$ 2 Choose the appropriate trigonometric ratio. $$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$$ 3 Substitute the values into the tangent equation. (Trigonometry, angle of elevation, height, distance, tangent function)

Step 1: Identify Given Information

We are given the distance from the base of the tower to the observation point, which is $18 \text{ m}$. We are also given the angle of elevation to the top of the tower, which is $30^\circ$. Our goal is to find the height of the tower, which we denote as $h$.

Step 2: Choose Trigonometric Ratio

Since we have a right-angled triangle formed by the tower, the ground, and the line of sight, and we know the adjacent side (distance from the base) and want to find the opposite side (height of the tower), the tangent function is the most appropriate trigonometric ratio to use.

Step 3: Substitute Values and Solve for Height

Substitute the given angle of elevation, $30^\circ$, and the adjacent side, $18 \text{ m}$, into the tangent formula. We know that $\tan(30^\circ) = \frac{1}{\sqrt{3}}$. Multiply both sides by $18$ to solve for $h$. Finally, rationalize the denominator to get the simplified height.

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