**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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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

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section3.3: Vectors In The Plane

Problem 78E: Velocity Pitcher Aroldis Chapman threw a pitch with a recorded velocity of 105 miles per hour....

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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 $.

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