In the diagram, AB is a vertical pole and BC is horizontal. If |AC| = 10m and |BC| = 5m, calculate the angle of depression of C from A

In the diagram, AB is a vertical pole and BC is horizontal. If |AC| = 10m and |BC| = 5m, calculate the angle of depression of C from A

Answer Details

The angle of depression of C from A is the angle formed between the line of sight from A to C and the horizontal line. This angle can be found using trigonometry. First, we can find the length of AB by using the Pythagorean theorem: |AB| = √(|AC|² - |BC|²) = √(10² - 5²) = √75 = 5√3 Next, we can find the tangent of the angle of depression: tan(θ) = |BC| / |AB| = 5 / (5√3) = √3 / 3 Finally, we can find the angle itself by taking the inverse tangent (or arctangent) of this value: θ = tan⁻¹(√3 / 3) ≈ 30° Therefore, the angle of depression of C from A is approximately 30°. The answer closest to this value is, 60°.