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To solve this problem, we can use trigonometry. Specifically, we’ll use the sine function, as we are given the angle of elevation and the opposite side (14 ft), and we need to find the hypotenuse (the length of the ladder).

### Given:
- Opposite side (\( h \)) = 14 ft
- Angle of elevation (\( \theta \)) = 71°
- We need to find the hypotenuse (\( L \)), which represents the ladder's length.

### Solution:
The sine function is defined as:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Rearranging to solve for the hypotenuse:
\[
L = \frac{\text{opposite}}{\sin(\theta)}
\]

Plugging in the values:
\[
L = \frac{14}{\sin(71^\circ)}
\]

Calculating this:
1. \(\sin(71^\circ) \approx 0.9455\).
2. Therefore, \(L = \frac{14}{0.9455} \approx 14.8\) ft.

### Answer:
The distance from the bottom of the ladder to the side of the house is approximately **14.8 ft**.

Would you like more details on this solution, or have any questions?

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Here are some related questions for further exploration:
1. How would the solution change if the angle were different, say 60°?
2. What trigonometric function would we use if we were given the hypotenuse and needed to find the adjacent side?
3. How can we calculate the horizontal distance from the ladder’s base to the house?
4. What is the significance of rounding in real-world measurements?
5. How does changing the ladder's angle of elevation affect its stability?

**Tip:** In right triangle problems involving angles, determine which trigonometric function (sine, cosine, or tangent) to use based on the sides you have and need to find.

A ladder leans against the side of a house. The angle of elevation of the ladder is 71°, and the top of the ladder is 14 ft above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.

Learn how to calculate the distance from the bottom of a ladder to the side of a house using trigonometric principles. With a 71° angle of elevation and a height of 14 ft, this problem demonstrates the application of the sine function to find distances in right triangles. Suitable for students in Grades 9-11.

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