The transportation department has to put a railing along the outer curve of this road. The road is 20 feet wide. What is the length of the outer curve to the nearest foot? Use the value 
 = 3.14.

A bending rectangular path width of 20 feet is marked, and a point marked, the outer side of the path with 50 feet and its angle of 70 degrees is marked.
 A. 
68 feet
 B. 
74 feet
 C. 
86 feet
 D. 
92 feet
 E. 
102 feet

To solve this problem, we need to calculate the length of the outer curve of the road. Since the path is part of a circle, we can use the formula for the length of an arc:

\[
\text{Arc Length} = r \cdot \theta
\]

where:
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.

### Step 1: Determine the radii
- The radius of the inner curve is \( r_{\text{inner}} = 50 \) feet.
- The width of the road is 20 feet, so the radius of the outer curve is \( r_{\text{outer}} = 50 + 20 = 70 \) feet.

### Step 2: Convert the angle from degrees to radians
- The central angle \( \theta \) is given as 70 degrees.
- To convert degrees to radians:

\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} = 70 \times \frac{3.14}{180} = 1.22 \text{ radians (approx)}
\]

### Step 3: Calculate the length of the outer curve
Using the outer radius \( r_{\text{outer}} = 70 \) feet and the angle in radians \( \theta = 1.22 \) radians:

\[
\text{Arc Length} = r_{\text{outer}} \times \theta = 70 \times 1.22 = 85.4 \text{ feet}
\]

### Step 4: Round to the nearest foot
The nearest whole number is 85 feet, which is closest to 86 feet.

### Final Answer
The length of the outer curve is approximately **86 feet**, which corresponds to option C.

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Would you like further details or have any questions? Here are some related questions to consider:

1. How do you calculate the arc length for different angles?
2. What are some practical applications of calculating arc lengths in real-world scenarios?
3. How do you convert angles between degrees and radians?
4. What is the relationship between the radius and arc length of a circle?
5. How would the arc length change if the road width was increased?

**Tip:** Always ensure the angle is in radians when using the formula \( \text{Arc Length} = r \cdot \theta \).

Learn how to calculate the length of the outer curve of a road using circle geometry. This problem involves determining the arc length with a given radius and central angle, applicable for high school geometry students.

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