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The problem states:

"Enyonam is standing on the roof of a building. The angle of depression from her to a car on the street is 30°. If Enyonam is 20 m above the street, how far away is the car from her?"

This is a trigonometric problem. We can solve it using the following steps:

1. **Identify the components of the problem**:
   - The height of the building (vertical distance) is \( 20 \, \text{m} \).
   - The angle of depression is \( 30^\circ \).
   - We are asked to find the horizontal distance from Enyonam to the car (the distance on the street).

2. **Use the tangent function**:
   Since the angle of depression is the angle between the line of sight and the horizontal, and we are dealing with a right triangle, we can apply the tangent formula:
   \[
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
   \]
   where:
   - \( \theta = 30^\circ \),
   - opposite = 20 m (the height of the building),
   - adjacent = the horizontal distance we are trying to find (let's call it \( d \)).

3. **Set up the equation**:
   \[
   \tan(30^\circ) = \frac{20}{d}
   \]

4. **Solve for \( d \)**:
   \[
   d = \frac{20}{\tan(30^\circ)}
   \]

I'll calculate that for you.The horizontal distance from Enyonam to the car is approximately \( 34.64 \, \text{m} \).

Would you like further details or have any questions?

Here are some related questions for further exploration:
1. What would happen if the angle of depression increased to 45°?
2. How would the calculation change if the building height doubled?
3. Can you use sine or cosine to solve this problem?
4. How can you interpret the tangent function in real-world situations?
5. What other angles of depression are commonly encountered in practical problems?

**Tip**: When dealing with right triangles and angles of elevation or depression, always identify the sides relative to the angle—opposite, adjacent, and hypotenuse—for correct trigonometric function use.

Enyonam is standing on the roof of a building. The angle of depression from her to a car on the street is 30°. If Enyonam is 20 m above the street, how far away is the car from her?

This problem explores how to calculate the horizontal distance between Enyonam and a car using trigonometry. Given a 30° angle of depression and a height of 20 meters, the solution involves the tangent function. Suitable for students in Grades 8-10.

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