Chalkboard Explanation Video Step-by-step Derivation 1 Identify the given information and unknown Distance from base $= 15 \text{ m}$ Angle of elevation $= 60^\circ$ Height of tower $= h = ?$ 2 Choose the appropriate trigonometric ratio $$\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}}$$ $$\tan 60^\circ = \frac{h}{15}$$ (Trigonometry, Angle of elevation, Tangent, Right triangle, Height)

Step 1: Identify Given Information

First, we identify the given information from the problem statement. We are given the distance from the base of the tower to the observation point, which is $15 \text{ m}$. We are also given the angle of elevation to the top of the tower, which is $60^\circ$. Our goal is to find the height of the tower, which we denote as $h$.

Step 2: Choose Trigonometric Ratio

To relate the height of the tower (opposite side) and the distance from the base (adjacent side) to the angle of elevation, we use the tangent trigonometric ratio. The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Step 3: Substitute Values and Solve for Height

Now, we substitute the given values into the tangent equation. The angle $\theta$ is $60^\circ$, the opposite side is $h$, and the adjacent side is $15 \text{ m}$. We know that $\tan 60^\circ = \sqrt{3}$. By rearranging the equation, we can solve for $h$.

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