An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. The ladder makes an angle of 71degrees 
∘
  with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

To solve for the length of the ladder, we can apply trigonometry. Specifically, we can use the sine function, which relates the angle, the length of the ladder (hypotenuse), and the height the ladder reaches on the wall (opposite side).

Given:
- Height (opposite side) = 28 feet
- Angle with the ground = 71°

We use the sine function:

\[
\sin(\theta) = \frac{{\text{{opposite}}}}{{\text{{hypotenuse}}}}
\]

Rearranging to solve for the hypotenuse (which is the length of the ladder):

\[
\text{{hypotenuse}} = \frac{{\text{{opposite}}}}{{\sin(\theta)}}
\]

Substitute the given values:

\[
\text{{hypotenuse}} = \frac{{28}}{{\sin(71^\circ)}}
\]

Now, calculate:

\[
\sin(71^\circ) \approx 0.9455
\]

\[
\text{{hypotenuse}} = \frac{{28}}{{0.9455}} \approx 29.61 \text{{ feet}}
\]

So, the length of the ladder is approximately **29.61 feet**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. How do we determine when to use sine, cosine, or tangent in trigonometry?
2. What other methods can you use to find the length of the ladder?
3. What would the length be if the angle were 60 degrees instead of 71?
4. How does changing the height affect the length of the ladder?
5. Can you calculate the base distance of the ladder from the wall?

**Tip:** Always check that your calculator is set to degrees, not radians, when solving problems with angles in degrees.

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 28 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.

Learn how to solve a trigonometry problem where an electrician leans a ladder against a house wall. The ladder reaches 28 feet up and makes a 71-degree angle with the ground. Use the sine function to calculate the ladder's length, suitable for students in Grades 9-12.

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