There is a ladder leaning up against a brick wall. The height of the wall is 12 feet. The length of the ladder is 13 feet. Which trigonometric tool should you use to determine what angle the ladder forms with the top of the wall? 13 ft 12 ft
There is a ladder leaning up against a brick wall. The height of the wall is 12 feet. The length of the ladder is 13 feet. Which trigonometric tool should you use to determine what angle the ladder forms with the top of the wall? 13 ft 12 ft
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
![**Determining the Angle of a Ladder Leaning Against a Wall Using Trigonometry**
There is a ladder leaning up against a brick wall. The height of the wall is 12 feet. The length of the ladder is 13 feet. Which trigonometric tool should you use to determine what angle the ladder forms with the top of the wall?
**Diagram Explanation:**
In the diagram, there is:
- A brick wall which is 12 feet tall, represented as a vertical line.
- A ladder that is 13 feet long, leaning against the wall.
- The angle θ, formed between the ladder and the top of the wall is shown.
To find this angle θ, we can use trigonometric functions such as sine, cosine, or tangent. Given that we know the length of the opposite side (12 feet) and the hypotenuse (13 feet), it is most appropriate to use the sine function, which relates the opposite side and the hypotenuse in a right-angled triangle.
**Calculation Steps:**
1. Using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(\theta) = \frac{12}{13} \]
2. To find θ:
\[ \theta = \sin^{-1}\left(\frac{12}{13}\right) \]
3. Compute the value:
\[ \theta ≈ 67.38^\circ \]
Therefore, the angle θ that the ladder forms with the top of the wall is approximately 67.38 degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F693046e0-0496-440e-a4a1-2d8d9c31eda7%2F66014477-fd59-4de8-a02f-6c4da59c45e9%2Farq1pl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining the Angle of a Ladder Leaning Against a Wall Using Trigonometry**
There is a ladder leaning up against a brick wall. The height of the wall is 12 feet. The length of the ladder is 13 feet. Which trigonometric tool should you use to determine what angle the ladder forms with the top of the wall?
**Diagram Explanation:**
In the diagram, there is:
- A brick wall which is 12 feet tall, represented as a vertical line.
- A ladder that is 13 feet long, leaning against the wall.
- The angle θ, formed between the ladder and the top of the wall is shown.
To find this angle θ, we can use trigonometric functions such as sine, cosine, or tangent. Given that we know the length of the opposite side (12 feet) and the hypotenuse (13 feet), it is most appropriate to use the sine function, which relates the opposite side and the hypotenuse in a right-angled triangle.
**Calculation Steps:**
1. Using the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(\theta) = \frac{12}{13} \]
2. To find θ:
\[ \theta = \sin^{-1}\left(\frac{12}{13}\right) \]
3. Compute the value:
\[ \theta ≈ 67.38^\circ \]
Therefore, the angle θ that the ladder forms with the top of the wall is approximately 67.38 degrees.
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