MACHINE SHOP CALCULATION - OD1640 - LESSON 2/TASK 3
(2) Squaring of AD procedure follows:
AD2
DB)2
=
(c
AD2
=
(c
DB)(c DB)
AD2
c2
cDB cDB + DB2
=
AD2
c2
2cDB + DB2
=
(3) Substituting AD2 into equation at (1) above:
b2 = c2
2cDB + DB2 + h2
(4) Equation for triangle 2, figure 27, view A (on the previous page):
a2 = h2 + DB2
(5) Finding the value of DB2:
DB2 + h2 = a2
DB2 + h2 - h2 = a2 h2
DB2 = a2 - h2
(6) Substituting DB2 into equation at (3) above:
According to the law of cosines,
b2 = a2 + c2 - 2ac Cos B.
b.
Since the result of the equation at (6) above and the law of cosines
both contain b2 , both equations, therefore, are equal.
Therefore:
(1) c2 - 2cDB + a2 = a2 + c2 - 2ac cos B
(2) Subtracting by -a2 - c2:
87
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