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Let's work through the problem step by step.

The problem involves a right triangle where:
- The angle of depression from the top of the school to the flagpole is 50°.
- The distance from the base of the school to the base of the flagpole is 35 feet.
- We need to find the height of the school.

### Steps to solve:
1. **Identify the triangle and the trigonometric relation**:
   The problem gives us a right triangle, with:
   - The horizontal distance (adjacent side) from the school to the flagpole = 35 feet.
   - The angle of depression from the top of the school to the flagpole = 50°.
   - We need to find the height of the school (opposite side).

2. **Use the tangent function**:
   The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. In this case, the tangent of 50° can be written as:
   \[
   \tan(50^\circ) = \frac{\text{height of the school}}{35}
   \]
   
   Solving for the height:
   \[
   \text{height of the school} = 35 \times \tan(50^\circ)
   \]

3. **Calculate the value**:
   We now compute the value for \(\tan(50^\circ)\) and multiply it by 35.

Let's calculate this now. math

# Given values
angle_degrees = 50
adjacent = 35

# Convert angle to radians and calculate the tangent
angle_radians = math.radians(angle_degrees)
height = adjacent * math.tan(angle_radians)

heightThe height of the school is approximately **41.7 feet**.

The correct answer is **E) 41.7 ft**.

Let me know if you would like further details or have additional questions! Here are some related questions to explore further:

1. How do we calculate the angle of depression if the height of the school and the distance are given?
2. What other trigonometric functions (sine and cosine) can be used to solve similar problems?
3. How can we apply these trigonometric principles in real-world scenarios?
4. Can this method be used for non-right triangles? If so, how?
5. What is the difference between the angle of depression and the angle of elevation?

**Tip**: When solving for heights in real-world problems, make sure to always draw a diagram to visualize the triangle and identify the correct sides for trigonometric ratios.

The angle of depression from the top of the school to the base of the flag pole in front of the school is 50°. If the flag pole is 35 feet from the base of the school, find the height of the school.

Learn how to solve a trigonometry problem where you find the height of a school using the tangent function. Given the angle of depression (50°) and the distance from the school to the flagpole (35 feet), the solution shows how to use the tangent formula to find that the height of the school is approximately 41.7 feet.

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