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A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3710-foot mountain. In 7 minutes, the angle of lepression to the leading edge of the fire changed from 0.88 radians to 1.16 radians. angle of depression a. How many feet does the fire advance during the 7 minutes the ranger observed the fire? feet Preview b. At what speed (in feet per minute) is the fire spreading towards the ranger?

A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3710-foot mountain. In 7 minutes, the angle of lepression to the leading edge of the fire changed from 0.88 radians to 1.16 radians. angle of depression a. How many feet does the fire advance during the 7 minutes the ranger observed the fire? feet Preview b. At what speed (in feet per minute) is the fire spreading towards the ranger?

Calculus: Early Transcendentals
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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### Forest Fire Observation Problem A forest ranger is observing the progress of a forest fire spreading towards her from the top of a 3710-foot mountain. Over the course of 7 minutes, the ranger notes that the angle of depression to the leading edge of the fire changes from 0.88 radians to 1.16 radians. #### Diagram Explanation The diagram shows a mountain with a height of 3710 feet. From the top of that mountain, lines are drawn downwards forming angles labeled as "angle of depression". The initial angle of depression (0.88 radians) shows the starting position of the fire line. The final angle of depression (1.16 radians) shows the new position of the fire line after the observed period of time. #### Questions **a. How many feet does the fire advance during the 7 minutes the ranger observed the fire?** **b. At what speed (in feet per minute) is the fire spreading towards the ranger?** #### Interactive Components - Input boxes for entering the distance the fire advanced in feet. - Input boxes for entering the speed of the fire spread in feet per minute. --- To answer the above questions, you will need to use trigonometric relationships to find the distances involved. Specifically, you can use the tangent of the angles of depression since tangent relates the height of the mountain to the distance of the fire from the base of the mountain.
Transcribed Image Text:### Forest Fire Observation Problem A forest ranger is observing the progress of a forest fire spreading towards her from the top of a 3710-foot mountain. Over the course of 7 minutes, the ranger notes that the angle of depression to the leading edge of the fire changes from 0.88 radians to 1.16 radians. #### Diagram Explanation The diagram shows a mountain with a height of 3710 feet. From the top of that mountain, lines are drawn downwards forming angles labeled as "angle of depression". The initial angle of depression (0.88 radians) shows the starting position of the fire line. The final angle of depression (1.16 radians) shows the new position of the fire line after the observed period of time. #### Questions **a. How many feet does the fire advance during the 7 minutes the ranger observed the fire?** **b. At what speed (in feet per minute) is the fire spreading towards the ranger?** #### Interactive Components - Input boxes for entering the distance the fire advanced in feet. - Input boxes for entering the speed of the fire spread in feet per minute. --- To answer the above questions, you will need to use trigonometric relationships to find the distances involved. Specifically, you can use the tangent of the angles of depression since tangent relates the height of the mountain to the distance of the fire from the base of the mountain.
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