A person stands on top of a 200 ft building and spots a person on the ground below. The angle of depression from where the person is standing on top of building to the person on the ground is 39º. How far away are the two people from each other? Round to the nearest foot. O 318 ft 257 ft 126 ft 247 ft
A person stands on top of a 200 ft building and spots a person on the ground below. The angle of depression from where the person is standing on top of building to the person on the ground is 39º. How far away are the two people from each other? Round to the nearest foot. O 318 ft 257 ft 126 ft 247 ft
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Trigonometry Problem: Calculating Distance Using Angle of Depression
A person stands on top of a 200 ft building and spots a person on the ground below. The angle of depression from where the person is standing on top of the building to the person on the ground is 39°. How far away are the two people from each other? Round to the nearest foot.
**Options:**
- A) 318 ft
- B) 257 ft
- C) 126 ft
- D) 247 ft
**Solution:**
To solve this problem, we will use trigonometric functions. Specifically, we will use the tangent function, which relates the angle of depression to the opposite and adjacent sides of the right triangle formed by the building height and the horizontal distance to the person on the ground.
Given:
- Height of the building (opposite side) = 200 ft
- Angle of depression = 39°
We need to find the distance between the two people, which is the adjacent side of the triangle.
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Here,
\[ \tan(39°) = \frac{200 \text{ ft}}{\text{adjacent}} \]
Solving for the adjacent side:
\[ \text{adjacent} = \frac{200 \text{ ft}}{\tan(39°)} \]
Using a calculator to find \( \tan(39°) \):
\[ \tan(39°) \approx 0.809 \]
Thus,
\[ \text{adjacent} = \frac{200 \text{ ft}}{0.809} \approx 247 \text{ ft} \]
So, the distance between the two people is approximately 247 feet.
The correct answer is:
- D) 247 ft](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F846a5d83-ebd2-4e0d-9bf0-b0f470211899%2F9c69974c-6876-488b-adb0-ee3e062552fb%2F1bpr1ie_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem: Calculating Distance Using Angle of Depression
A person stands on top of a 200 ft building and spots a person on the ground below. The angle of depression from where the person is standing on top of the building to the person on the ground is 39°. How far away are the two people from each other? Round to the nearest foot.
**Options:**
- A) 318 ft
- B) 257 ft
- C) 126 ft
- D) 247 ft
**Solution:**
To solve this problem, we will use trigonometric functions. Specifically, we will use the tangent function, which relates the angle of depression to the opposite and adjacent sides of the right triangle formed by the building height and the horizontal distance to the person on the ground.
Given:
- Height of the building (opposite side) = 200 ft
- Angle of depression = 39°
We need to find the distance between the two people, which is the adjacent side of the triangle.
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Here,
\[ \tan(39°) = \frac{200 \text{ ft}}{\text{adjacent}} \]
Solving for the adjacent side:
\[ \text{adjacent} = \frac{200 \text{ ft}}{\tan(39°)} \]
Using a calculator to find \( \tan(39°) \):
\[ \tan(39°) \approx 0.809 \]
Thus,
\[ \text{adjacent} = \frac{200 \text{ ft}}{0.809} \approx 247 \text{ ft} \]
So, the distance between the two people is approximately 247 feet.
The correct answer is:
- D) 247 ft
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