An Ancient Chinese Problem This problem is taken from aChinese mathematics textbook called Chui-chang suan-shu,or Nine Chapters on the Mathematical Art, which was writ-ten about 250 B.C.A 10-ft-long stem of bamboo is broken in such a waythat its tip touches the ground 3 ft from the base of thestem, as shown in the figure. What is the height of thebreak?[Hint: Use the Pythagorean Theorem.]3 ft

Let's assume height of break is x ft We know that in a right angle triangle…

Answered: An Ancient Chinese Problem This problem…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.9: Modeling With Equations

Problem 68E: An Ancient Chinese Problem The problem is taken from a Chinese mathematics textbook called...

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APPLICATIONS An Ancient Chinese Problem This problem is taken from a Chinese mathematics textbook called Chui-Chang suan-shu, or Nine Chapters on the Mathematical Art, which was written about 250 B.C. A 10-ft-long stem of bamboo is broken in such a way that its tip touches the ground 3 ft from the base of the stem, as shown in the figure. What is the height of the break? Hint: Use the Pythagorean Theorem
An artist wants to make a small monument in the shape of a square base topped by a right triangle, as shown below. The square base will be adjacent to one leg of the triangle. The other leg of the triangle will measure 2 feet and the hypotenuse will be 5 feet. (a) Use the Pythagorean Theorem to find the length of a side of the square base. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the face of the square base.
A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.
Plans call for triangle BCDto be sheared off a corner of a rectangle as shown in the figure. A decision is made to move one vertex of the triangle 1.5 in. from B to B' and the other vertex from D to D'. How much larger is the area of AB' D' than ABDEF ?
A cross section of an aluminum bar in the shape of a trapezoid is shown. All the dimensions are in inches. a. Find the cross-sectional area of the bar. b. Find the length of side AB. Round the answer to the nearest hundredth inch.
Height of a Tree You measure a tree’s shadow and find that it is 8 meters long. Then you measure the shadow of a nearby two-meter lamppost and find that it is 75 centimeters long. (See figure.) How tall is the tree?
The Unified Thread may have either a flat or rounded crest or root (Figure 4-6). If the sides of the Unified Thread are extended, a sharp V-thread is formed (Figure 4-7). In Figure 4-7, H is the height of a sharp V-thread. The pitch, P, is the distance between two adjacent threads. Find dimensions A, B, and C as indicated. a. H=716A=_,B=_ b. H=38A=_,B=_ c. H=1516A=_,B=_ d. H=2132A=_,B=_ e. H=34A=_,B=_ f. P=14C=_ g. P=332C=_ h. P=120C=_ i. P=128C=_ j. P=316C=_
Finding Dimensions At a glassware factory, molten cobalt glass is poured into molds to make paperweights. Each mold is a rectangular prism whose height is 3inches greater than the length of each side of the square base. A machine pours 20cubic inches of liquid glass into each mold. What are the dimensions of the mold?
Width of a Lawn A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?

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