USEFUL FORMULAS. 



XIX 



In right angled triangles let 



Then 



a = altitude, 



l> = base, 



c = hypothenuse, 



7 = 9°°- 



a = c sin a = <r cos ^ = b tan a : 

 I) = c sin /3 ^= c cos a = a tan (3 



A -^ \ a I) =. \ a- cot a = ^ ^^ tan a = 



b cot ^, 



: a cot a. 



J^ r sin 2 a. 



Table for soluHon of oblique triangles. 



Given. 



a, b, c 



a, b, a 



a, a, /5 



a, b, y 



Sought. 



ys 



y 



y 



A 



a 



Formula. 



sin ^ a : 



COS ^ a 



tan ^ a 

 A 



. (,, ^ /. 4- ^), 



— \/ s(s — a) (s — b) (s — e) 



sin /3 = b sin a/a. 



When ay b, ji < 90° and but one value results. When b> a, 



P has two values. 

 y = 180° - (a + i8). 

 e z=z a sin y/sin a. 

 A= h a b sin y. 



b =^ a sin (3/sin a, 



y = 180° - (a + /3). 



c := a sin y/sin a = ^ sin (a -f- /3)/sin a. 



.^=: i- fl! ^ sin y = ^ a'^ sin ^ sin y/sin a. 



tan a = 



a sin y 



b — a cos y 



tan ^ (a - /3) = ^^^p, cot I y. 



(■ = (a- -|- ^^ — 2 a ^ cos y)-, 



= {(a -\- b)- — 4 a b cos- ^ y}^ 



:= {(a — b)--\- 4. a b sin" i y}*, 



= (<•? — b)/cos cf), where tan ^ = 2 ^/ab sin ^ y/(<3! 



= a sin y/sin a. 

 y/ = ^ a b sin y. 



-^), 



