A 15 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree. -0. S 15 14 X/ X=
A 15 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree. -0. S 15 14 X/ X=
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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![**Problem:**
A 15 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground. Find \( x \), the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
**Solution:**
We will use trigonometry to solve for the angle of elevation \( x \).
**Diagram Explanation:**
There is a right triangle in the diagram with:
- The ladder forming the hypotenuse (15 ft),
- The height from the ground to the top of the ladder against the house forming the opposite side (14 ft),
- The ground distance from the bottom of the ladder to the house, forming the adjacent side.
**Mathematical Approach:**
To find the angle of elevation \( x \), we use the sine function:
\[ \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{14}{15} \]
Using a calculator to find the inverse sine (arcsin):
\[ x = \arcsin\left(\frac{14}{15}\right) \approx 69.4^\circ \]
**Answer:**
The angle of elevation of the ladder is approximately \( 69.4^\circ \).
**Interactive Section:**
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**Note:** The solution is rounded to the nearest tenth of a degree.
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Transcribed Image Text:**Problem:**
A 15 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground. Find \( x \), the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
**Solution:**
We will use trigonometry to solve for the angle of elevation \( x \).
**Diagram Explanation:**
There is a right triangle in the diagram with:
- The ladder forming the hypotenuse (15 ft),
- The height from the ground to the top of the ladder against the house forming the opposite side (14 ft),
- The ground distance from the bottom of the ladder to the house, forming the adjacent side.
**Mathematical Approach:**
To find the angle of elevation \( x \), we use the sine function:
\[ \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{14}{15} \]
Using a calculator to find the inverse sine (arcsin):
\[ x = \arcsin\left(\frac{14}{15}\right) \approx 69.4^\circ \]
**Answer:**
The angle of elevation of the ladder is approximately \( 69.4^\circ \).
**Interactive Section:**
- An input box to let users try calculating or verifying their responses.
- Buttons labeled 'x', '⤬', and '?', possibly for verification, submission, and help.
**Note:** The solution is rounded to the nearest tenth of a degree.
**Actions:**
- Continue with the provided response.
- Option to submit your assignment using the "Submit Assignment" button.
**Terms of Use and Privacy:**
Ensure to review and adhere to the provided Terms of Use and Privacy Center information typically displayed at the bottom of the webpage.
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