A ladder 38.9 feet long reaches to the top of a building when its foot stands 11.6 feet from the building. How high is the building? The building is feet tall.
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![**Problem Statement**
A ladder 38.9 feet long reaches to the top of a building when its foot stands 11.6 feet from the building. How high is the building?
**Response Box**
The building is [ ] feet tall.
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**Explanation and Solution**
This problem involves using the Pythagorean theorem to determine the height of the building. Consider the ladder, the distance from the base of the building to the foot of the ladder, and the height of the building as the sides of a right triangle.
- The ladder (hypotenuse) = 38.9 feet
- The distance from the building to the ladder (base) = 11.6 feet
- The height of the building (perpendicular) = unknown
The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the base (11.6 feet),
- \( b \) is the height of the building,
- \( c \) is the hypotenuse (38.9 feet).
Using this formula, you can solve for the height (b):
\[ 11.6^2 + b^2 = 38.9^2 \]
\[ b^2 = 38.9^2 - 11.6^2 \]
\[ b = \sqrt{38.9^2 - 11.6^2} \]
After performing the calculations, you will find the height of the building.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc41fe58f-b2db-440f-b30c-6e46891d2c1e%2F89d518d0-27b1-451b-a1bf-59fe14eae9d3%2Fty3kl0i_processed.jpeg&w=3840&q=75)
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