KIT 



CHECKS ON COMPUTATIONS IX THE SOLUTION OF TRIANGLES 

 A. M. KENYON 



It is tlio purpose of this note to illustrate methods of chocking the accuracy of the 

 results when unknown parts of plane triangles are computed from given parts. Five 

 place tables are used in the computations. 



I. RIOHT TRIANOLES. 



Let fi represent the liypoteuuse and a and h the other two sides of a right ti'iaiigic 

 Let R be the right angle and A and D the acute angles opposite a and h respecnively • 

 To fix ideas suppose A is not less than B. 



Either of the following identities contains all five of the variable parts and can 

 be used as a check formula when a right triangle has been completely solved. 



(1) 2 «& = /i2 COS (-l-B) 



(2) (a+b) (a-b) ^ ]V- sin {A-B) 



To prove these produce AR (Fig. 1) to C making RC = AR, connect ZJC, and ilraw 

 VD perpendicular to AB. Then CB =^ h and angle BCD ^=^ A-B. 



CD = /( cos (A-B) = 2b sin A 



Tliorofore h'i cos (A-B) = 2bh sin .4 = 2ub 



DB ~ h sin (.A-B) = h -26 cos A 



Therefore /j" sin (.4-B) = h^~2bh C05 A = a^-b^ 



It is evident that these formulas hold also when A is less than B. 

 If it is desired to check only the sides, either of the formulas 



(3) 



(/i+&) (/i-6)or&2= ih+a) (,h-a) 



may be used. 



