A police department has set up a speed enforcement zone on a straight length of highway. A patrol car is parked parallel to the zone, 200 feet from one end and 150 feet from the other end (see figure). Enforcement zone 200 ft 150 ft Not drawn to scale (a) Find the length / of the zone and the measures of the angles A and B (in degrees). (Round your answers to two decimal places.) ft A = B = (b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 45 miles per hour. (Round your answer to two decimal places.) sec
A police department has set up a speed enforcement zone on a straight length of highway. A patrol car is parked parallel to the zone, 200 feet from one end and 150 feet from the other end (see figure). Enforcement zone 200 ft 150 ft Not drawn to scale (a) Find the length / of the zone and the measures of the angles A and B (in degrees). (Round your answers to two decimal places.) ft A = B = (b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 45 miles per hour. (Round your answer to two decimal places.) sec
Calculus: Early Transcendentals
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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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Question
In the diagram:
- The enforcement zone is represented by the segment labeled \( l \).
- A patrol car is observed from two points, one 200 feet from one end and one 150 feet from the other end which create angles \( A \) and \( B \).
**Tasks:**
(a) Find the length \( l \) of the zone and the measures of the angles \( A \) and \( B \) (in degrees). (Round your answers to two decimal places.)
\[ l = \_\_\_\_\_ \text{ ft} \]
\[ A = \_\_\_\_\_{}^\circ \]
\[ B = \_\_\_\_\_{}^\circ \]
(b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 45 miles per hour. (Round your answer to two decimal places.)
\[ \_\_\_\_\_ \text{ sec} \]
---
### Explanation of the Diagram
The diagram shown depicts a straight length of a highway designated as an "Enforcement Zone." The zone is a section between two points on the highway where the speed enforcement is active.
- The distance from the left end of the zone to the patrol car is given as 200 feet.
- The distance from the right end of the zone to the patrol car is given as 150 feet.
A dashed line represents these distances. These two distances form a triangle with the zone length \( l \) as the base, creating the angles \( A \) and \( B \) at the patrol car’s location.
---
To solve part (a):
1. Use the given distances to form a right-angled triangle with \( l \) and its components.
2. Apply trigonometric functions (like sine, cosine, tangent) to find the length \( l \) and angles \( A \) and \( B \).
For part (b):
1. Convert the speed limit from miles per hour to feet per second.
2. Use the formula \( \text{Time} = \frac{\text{Distance](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fab864d-7419-4b8c-bc50-25971d273c3c%2F4b71aca2-138a-4511-9cfa-bc729c316ec2%2Fcyg4rxb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Speed Enforcement Problem
**Problem Statement:**
A police department has set up a speed enforcement zone on a straight length of highway. A patrol car is parked parallel to the zone, 200 feet from one end and 150 feet from the other end (see figure).
In the diagram:
- The enforcement zone is represented by the segment labeled \( l \).
- A patrol car is observed from two points, one 200 feet from one end and one 150 feet from the other end which create angles \( A \) and \( B \).
**Tasks:**
(a) Find the length \( l \) of the zone and the measures of the angles \( A \) and \( B \) (in degrees). (Round your answers to two decimal places.)
\[ l = \_\_\_\_\_ \text{ ft} \]
\[ A = \_\_\_\_\_{}^\circ \]
\[ B = \_\_\_\_\_{}^\circ \]
(b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 45 miles per hour. (Round your answer to two decimal places.)
\[ \_\_\_\_\_ \text{ sec} \]
---
### Explanation of the Diagram
The diagram shown depicts a straight length of a highway designated as an "Enforcement Zone." The zone is a section between two points on the highway where the speed enforcement is active.
- The distance from the left end of the zone to the patrol car is given as 200 feet.
- The distance from the right end of the zone to the patrol car is given as 150 feet.
A dashed line represents these distances. These two distances form a triangle with the zone length \( l \) as the base, creating the angles \( A \) and \( B \) at the patrol car’s location.
---
To solve part (a):
1. Use the given distances to form a right-angled triangle with \( l \) and its components.
2. Apply trigonometric functions (like sine, cosine, tangent) to find the length \( l \) and angles \( A \) and \( B \).
For part (b):
1. Convert the speed limit from miles per hour to feet per second.
2. Use the formula \( \text{Time} = \frac{\text{Distance
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