Transformational Plane Geometry 1st Edition Umble Solutions Manual 2.

26/06/2020




PLANE GEOMETRY d




ENGR.dLOUIEdA.dALCANTARA,dCE,dMP




𝑇𝑅𝐼𝐴𝑁𝐺𝐿𝐸𝑆(𝑃𝑎𝑟𝑡d1):
𝐶𝐴𝑆𝐸d1: 𝐶𝐴𝑆𝐸d 2: 𝐶𝐴𝑆𝐸d3:


𝑎
ℎ ℎ
𝜃


𝑏 𝑏 𝑏
1 1 1
𝐴d =d 𝑏ℎ 𝐴d = 𝑎𝑏𝑠𝑖𝑛𝜃
2d 2
𝐴d =d 𝑏
2d
ℎ

𝐶𝐴𝑆𝐸d 4:

Heron’dsdformula:
𝐴d = 𝑆d 𝑠d −d𝑎d d 𝑠d −d𝑏d (𝑠d−d𝑐)
𝑎 𝑐
𝑎+𝑏+𝑐
Where:d Sd=
2
Sd=dsemi-perimeter
𝑏




1

, 26/06/2020




Twodsidesdofdadtriangledmeasured36dmdandd49dm.dOnedpossibleddimensiondofdthe
dthirddsidedis

84dm c.d d 85dm
12dm d.d d 13dm

Solution:
ad=d49dm
bd=d36dm
c?
Trydcd=dad+db
cd=d49d+d36d=d85 cd=d85


ad=d49

bd=d36dm bd=d36dm ad=d49
cd=d85
cd=d85
cd=d85




Trydcd>d(ad+db) Trydcd<d(ad+db)

cd>d85 cd<d85
cd=d100 cd=d80

ad=d49

bd=d36dm

cd=d100
cd=d80




cd=d100

cd=d80

cd<d85
cd=d100 cd<d(ad+db
)




2

, 26/06/2020




ad=d49dm
bd=d36dmdc
?
Trydcd=dad-db
cd=d49d-d36d=d13

ad=d49
ad=d49
bd=d36dm

bd=d36dm cd=d13
cd=d13
ad=d49


cd=d13




ad=d49dm
bd=d36dm
dc?

Trydcd<d(ad–
db)dcd<d13




ad=d49
ad=d49
bd=d36dm

cd=d5
ad=d49


cd<d13




3

, 26/06/2020




ad=d49dm
bd=d36dm
dc?

Trydcd>d(ad–
db)dcd >d1

3

a = 49 ad=d49
bd=d36dm

cd=d20




ad=d49


cd>d(ad-db)




(ad–db)d<d cd<d(ad+db)

13d<d cd<d85


a. 84dm c. 85dm
b. 12dm d. 13dm


Cd=d84dm




4