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The problem asks for the angle that the staircase makes with the ground, given the following measurements:
- The width (run) of each step is 15 cm.
- The height (rise) of each step is 10 cm.

This scenario forms a right triangle where:
- The run (horizontal leg) is 15 cm.
- The rise (vertical leg) is 10 cm.
- The angle \(\theta\) (the angle the staircase makes with the ground) is opposite to the rise and adjacent to the run.

We can use the tangent function to calculate \(\theta\):

\[
\tan(\theta) = \frac{\text{opposite (rise)}}{\text{adjacent (run)}} = \frac{10}{15}
\]

Now, calculate \(\theta\):

\[
\theta = \tan^{-1} \left(\frac{10}{15}\right)
\]

\[
\theta \approx \tan^{-1} (0.6667) \approx 33.69^\circ
\]

So, the angle the staircase makes with the ground is approximately **33.69 degrees**.

Do you need further details or have any questions?

Here are 5 related questions:
1. How would the angle change if the rise increased but the run stayed the same?
2. What is the length of the hypotenuse (the slope of the staircase)?
3. How could you calculate the number of steps if you know the total height and this step design?
4. How does increasing both rise and run proportionally affect the angle?
5. How can the cosine or sine of the angle be used to verify the result?

**Tip:** The angle of elevation can be estimated using basic trigonometric ratios whenever you have height and base information of right triangles.

A staircase is to be built so that the width (run) of each step is 15 cm and the height (rise) of each step is 10 cm. What angle will the staircase make with the ground?

Learn how to calculate the angle that a staircase makes with the ground using trigonometric functions. This problem involves a staircase with a 15 cm run and a 10 cm rise, applying the tangent function to determine the angle. Suitable for students in Grades 8-10.

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