Claire climbs 550 feet to the top of a monument. She looks down and sees her friend, who is standing at point B in the diagram. What is the measure of the angle of depression, A, from Claire to her friend. (Round to two decimal places) 150 ft A. 550
Claire climbs 550 feet to the top of a monument. She looks down and sees her friend, who is standing at point B in the diagram. What is the measure of the angle of depression, A, from Claire to her friend. (Round to two decimal places) 150 ft A. 550
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
![**Calculating the Angle of Depression**
Claire climbs 550 feet to the top of a monument. She looks down and sees her friend, who is standing at point B in the diagram. What is the measure of the angle of depression, \( A \), from Claire to her friend? (Round to two decimal places)
*Figure Description:*
The diagram consists of a right-angled triangle:
- Point A represents the top of the monument where Claire is located.
- Point B represents the position of Claire's friend at ground level.
- The vertical distance (height of the monument) from A to the ground level is 550 feet.
- The horizontal distance between Claire's position (vertically above point B) and point B is 150 feet.
- A line is drawn from A to B indicating Claire's line of sight to her friend.
To solve for the angle of depression, \( A \), we use the tangent function in trigonometry, which relates the angle to the ratio of the opposite side (height) and the adjacent side (base) of the right triangle:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{550 \text{ ft}}{150 \text{ ft}}
\]
By calculating the above ratio:
\[
\tan(A) = \frac{550}{150} \approx 3.67
\]
Next, we find the angle \( A \) whose tangent is 3.67 using the inverse tangent function (\(\tan^{-1}\) or \(\arctan\)):
\[
A \approx \tan^{-1}(3.67) \approx 74.64^\circ
\]
Therefore, the angle of depression from Claire to her friend is approximately \( 74.64^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6f28f84-dd49-4a54-a5c4-242d0454d6ea%2Fe20839ce-bea9-49f1-9434-aec9a0242e82%2Fmzv4mg8_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating the Angle of Depression**
Claire climbs 550 feet to the top of a monument. She looks down and sees her friend, who is standing at point B in the diagram. What is the measure of the angle of depression, \( A \), from Claire to her friend? (Round to two decimal places)
*Figure Description:*
The diagram consists of a right-angled triangle:
- Point A represents the top of the monument where Claire is located.
- Point B represents the position of Claire's friend at ground level.
- The vertical distance (height of the monument) from A to the ground level is 550 feet.
- The horizontal distance between Claire's position (vertically above point B) and point B is 150 feet.
- A line is drawn from A to B indicating Claire's line of sight to her friend.
To solve for the angle of depression, \( A \), we use the tangent function in trigonometry, which relates the angle to the ratio of the opposite side (height) and the adjacent side (base) of the right triangle:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{550 \text{ ft}}{150 \text{ ft}}
\]
By calculating the above ratio:
\[
\tan(A) = \frac{550}{150} \approx 3.67
\]
Next, we find the angle \( A \) whose tangent is 3.67 using the inverse tangent function (\(\tan^{-1}\) or \(\arctan\)):
\[
A \approx \tan^{-1}(3.67) \approx 74.64^\circ
\]
Therefore, the angle of depression from Claire to her friend is approximately \( 74.64^\circ \).
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