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.