A staircase is  23.1-feet high and  27.3-feet at the base. Determine the angle from its base to the top. Round to the nearest tenth of a degree. 

To determine the angle from the base to the top of the staircase, we can treat this problem as a right triangle, where:

- The height of the staircase is 23.1 feet (opposite side).
- The base of the staircase is 27.3 feet (adjacent side).

We will use the tangent function in trigonometry because the tangent of an angle is the ratio of the opposite side to the adjacent side:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Thus, the angle \(\theta\) is:

\[
\theta = \tan^{-1}\left(\frac{23.1}{27.3}\right)
\]

Now, let's calculate the angle \(\theta\).The angle from the base to the top of the staircase is approximately **40.2 degrees**.

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. How would the angle change if the base of the staircase were longer?
2. What is the length of the hypotenuse of the staircase?
3. How would you calculate the area of the right triangle formed by the staircase?
4. Can you determine the angle if only the height and hypotenuse are known?
5. How would the angle affect the steepness of the staircase?

**Tip:** In any right triangle, using different trigonometric ratios like sine, cosine, and tangent helps solve for various unknowns depending on which sides are known.

A staircase is 23.1-feet high and 27.3-feet at the base. Determine the angle from its base to the top. Round to the nearest tenth of a degree.

Learn how to find the angle of elevation of a staircase that is 23.1 feet high and has a base of 27.3 feet. This trigonometry problem uses the tangent function and the inverse tangent theorem to calculate the angle, suitable for students in Grades 9-11.

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