### 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).![Speed Enforcement Diagram](speed_enforcement_diagram.jpg)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 DiagramThe 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

Answered: Image /qna-images/answer/4b71aca2-138a-4511-9cfa-bc729c316ec2.jpg

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

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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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

### 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).

![Speed Enforcement Diagram](speed_enforcement_diagram.jpg)

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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