21. A boat is 200 m away from the base of a cliff.The angle of depression from the top of the cliff to the boat is 18^circ What is the angle of elevation from the boat to the top of the cliff?Calculate the height of the cliff to the nearest metre.

## Step 1: Finding the Angle of Elevation<br />### The angle of elevation from the boat to the top of the cliff is equal to the angle of depression from the top of the cliff to the boat. This is because they are alternate interior angles formed by a transversal (the line of sight) intersecting two parallel lines (the horizontal line from the top of the cliff and the horizontal line from the boat).<br />## Step 2: Calculating the Height of the Cliff<br />### We can use the tangent function to relate the angle of elevation, the distance from the boat to the cliff, and the height of the cliff. Let $h$ be the height of the cliff and $d$ be the distance from the boat to the cliff. We have $\tan(\theta) = \frac{h}{d}$, where $\theta$ is the angle of elevation. Given $d = 200$ m and $\theta = 18^{\circ}$, we can solve for $h$: $h = d \times \tan(\theta) = 200 \times \tan(18^{\circ}) \approx 200 \times 0.3249 \approx 64.98$ m. Rounding to the nearest meter, the height is approximately 65 m.