Question

find angles of depression and elevation. 12 feet, 12√3, horizontal, angle of elevation, angle of depression, line of sight

Explanation:

Step1: Identify the triangle type

We have a right - triangle with opposite side (height) = 12 feet and adjacent side (horizontal distance) = $12\sqrt{3}$ feet. We can use the tangent function, where $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Calculate the angle of elevation

Let the angle of elevation be $\theta$. Then $\tan\theta=\frac{12}{12\sqrt{3}}=\frac{1}{\sqrt{3}}$. We know that $\tan30^{\circ}=\frac{1}{\sqrt{3}}$, so $\theta = 30^{\circ}$.

Step3: Analyze the angle of depression

The angle of depression and the angle of elevation are equal (alternate interior angles) because the horizontal lines are parallel. So the angle of depression is also $30^{\circ}$.

Answer:

The angle of elevation is $30^{\circ}$ and the angle of depression is $30^{\circ}$.