Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 65 degrees, how far is the bottom of the ladder from the base of the building? (Round to two decimal places)
Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 65 degrees, how far is the bottom of the ladder from the base of the building? (Round to two decimal places)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![**Problem Statement:**
Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 65 degrees, how far is the bottom of the ladder from the base of the building? (Round to two decimal places)
**Diagram Explanation:**
The image accompanying this problem depicts a right triangle. The hypotenuse of the triangle represents the ladder, which measures 10 feet. The angle between the hypotenuse (ladder) and the adjacent side (the distance from the base of the ladder to the building) is given as 65 degrees. The adjacent side is marked with a question mark indicating the unknown value that we need to calculate.
To solve this problem, you can use the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Given:
- \(\theta = 65^\circ\)
- Hypotenuse = 10 ft
Set up the equation:
\[ \cos(65^\circ) = \frac{\text{adjacent}}{10 \text{ ft}} \]
Solve for the adjacent side (bottom of the ladder from the base of the building):
\[ \text{adjacent} = 10 \text{ ft} \times \cos(65^\circ) \]
Make sure to round your final answer to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6f28f84-dd49-4a54-a5c4-242d0454d6ea%2F9a28e9c7-6110-4b15-92bc-752de4afa5a3%2Fs2rwuxu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 65 degrees, how far is the bottom of the ladder from the base of the building? (Round to two decimal places)
**Diagram Explanation:**
The image accompanying this problem depicts a right triangle. The hypotenuse of the triangle represents the ladder, which measures 10 feet. The angle between the hypotenuse (ladder) and the adjacent side (the distance from the base of the ladder to the building) is given as 65 degrees. The adjacent side is marked with a question mark indicating the unknown value that we need to calculate.
To solve this problem, you can use the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Given:
- \(\theta = 65^\circ\)
- Hypotenuse = 10 ft
Set up the equation:
\[ \cos(65^\circ) = \frac{\text{adjacent}}{10 \text{ ft}} \]
Solve for the adjacent side (bottom of the ladder from the base of the building):
\[ \text{adjacent} = 10 \text{ ft} \times \cos(65^\circ) \]
Make sure to round your final answer to two decimal places.
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