City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank a miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. (See the figure below.) City A L P= 1 mile a miles City B You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Length of one leg2+ Length of other leg² Length of hypotenuse (a) If a 8, use an appropriate right triangle to find a formula for W in terms of L. (b) Find a formula for the length of the total phone cable P from City A to City B as a function of L

City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank a miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. (See the figure below.) City A L P= 1 mile a miles City B You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Length of one leg2+ Length of other leg² Length of hypotenuse (a) If a 8, use an appropriate right triangle to find a formula for W in terms of L. (b) Find a formula for the length of the total phone cable P from City A to City B as a function of L

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank a miles down the river. You will lay L miles of the
cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. (See the figure below.)
City A
1 mile
10
a miles
You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the
Pythagorean theorem, relates the lengths of the three sides:
Length of hypotenuse = √Length of one leg2+ Length of other leg².
(a) If a 8, use an appropriate right triangle to find a formula for W in terms of L.
8
City B
(b) Find a formula for the length of the total phone cable P from City A to City B as a function of L.
(c) Make a graph of the total phone cable length P as a function of L.
P
10

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