Question

Suppose you are shooting an arrow from the top of a building of height 6 m to a target on the ground at an angle of depression of $60^\circ$. What is the distance between you and the object?

• A. $2\sqrt{3}$ m
• B. $8\sqrt{3}$ m
• C. $16$ m
• D. $4\sqrt{3}$ m

Hint:

Angle of depression problems usually form a right triangle. Always identify whether you need sin, cos, or tan based on given sides.

Answer 1

The Correct Option is D

Concept: Angle of depression from the top of a building equals angle of elevation from the ground. The situation forms a right triangle where:
• Height of building = opposite side
• Distance between observer and target = hypotenuse We use: \[ \sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \]

Step 1: Identify values.
\[ \text{Height} = 6 \text{ m}, \quad \theta = 60^\circ \]

Step 2: Apply sine ratio.
\[ \sin 60^\circ = \frac{6}{AC} \] \[ \frac{\sqrt{3}}{2} = \frac{6}{AC} \]

Step 3: Solve for AC.
\[ AC = \frac{12}{\sqrt{3}} \]

Step 4: Rationalize denominator.
\[ AC = \frac{12\sqrt{3}}{3} = 4\sqrt{3} \] Conclusion: \[ \boxed{4\sqrt{3}\ \text{m}} \]