3. Find the angle of elevation of the sun if a building 125 feet tall casts a shadow 196 feet long. Round to the nearest degree. O. A. 40" B. 33" C. 50° D. 64"
3. Find the angle of elevation of the sun if a building 125 feet tall casts a shadow 196 feet long. Round to the nearest degree. O. A. 40" B. 33" C. 50° D. 64"
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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Need to find angle
![### Elevation Angle of the Sun: A Mathematics Exercise
In this problem, we are asked to determine the angle of elevation of the sun. The scenario provided involves a building that is 125 feet tall and casts a shadow that is 196 feet long. To solve for the angle of elevation, we must round our answer to the nearest degree.
**Question:**
> 3. Find the angle of elevation of the sun if a building 125 feet tall casts a shadow 196 feet long. Round to the nearest degree.
**Options:**
- A. \(40^\circ\)
- B. \(33^\circ\)
- C. \(50^\circ\)
- D. \(64^\circ\)
To solve this, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this context:
- Opposite side (height of the building) = 125 feet
- Adjacent side (length of the shadow) = 196 feet
Thus, we calculate the angle \( \theta \) by:
\[ \theta = \tan^{-1}\left(\frac{125}{196}\right) \]
Performing the calculation:
\[ \theta \approx \tan^{-1}(0.6378) \]
\[ \theta \approx 32.77^\circ \]
Rounded to the nearest degree, the angle of elevation of the sun is:
\[ \theta \approx 33^\circ \]
So, the correct answer is:
**B. \(33^\circ\)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6756c5c2-608f-4015-b13f-deb910f8c3e1%2Fb619727a-cf12-4156-b495-7200f096a211%2Fu723rc8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Elevation Angle of the Sun: A Mathematics Exercise
In this problem, we are asked to determine the angle of elevation of the sun. The scenario provided involves a building that is 125 feet tall and casts a shadow that is 196 feet long. To solve for the angle of elevation, we must round our answer to the nearest degree.
**Question:**
> 3. Find the angle of elevation of the sun if a building 125 feet tall casts a shadow 196 feet long. Round to the nearest degree.
**Options:**
- A. \(40^\circ\)
- B. \(33^\circ\)
- C. \(50^\circ\)
- D. \(64^\circ\)
To solve this, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this context:
- Opposite side (height of the building) = 125 feet
- Adjacent side (length of the shadow) = 196 feet
Thus, we calculate the angle \( \theta \) by:
\[ \theta = \tan^{-1}\left(\frac{125}{196}\right) \]
Performing the calculation:
\[ \theta \approx \tan^{-1}(0.6378) \]
\[ \theta \approx 32.77^\circ \]
Rounded to the nearest degree, the angle of elevation of the sun is:
\[ \theta \approx 33^\circ \]
So, the correct answer is:
**B. \(33^\circ\)**.
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