Then 



XVIU USEFUL FORMULAS. 



Put 180° „ , . , 



= /3 = number of degrees in the radius, 

 ^ p' = number of minutes in the radius, 

 = p" = number of seconds in the radius. 

 X° = X p°, x' ■=. X p, x" = X p". 



P° = 57-°2957795. log p° = 1.75812263, 



P = 3437-'74677, log p' = 3.53627388, 



p"=: 2o6264."8o6, log p" = 5.31442513. 



3. Formulas for Solution of Plane Triangles. 



a, b, c =^ sides of triangle, 



a.^ ^,y^ angles opposite to a, b, c, respectively, 

 A = area of triangle, 

 r = radius of inscribed circle, 

 R = radius of circumscribed circle, 

 s = h (d '\- b -\- c). 



a b c 



= -^-r. = -■ = 2 i?. 



sin a sin (^ sin y 



a ^ b cos y -\- (^ cos /?, b = c cos a -\- a cos y, c =^ a cos /3 -\- b cos a, 



ri • • r, • a b c 



f'=4 A sin 1 a sin ^ p sin i y = — tj— • 



{a -f- ii^) cos ^ (a -}- /3) = <r cos \ {a. — /?), 

 (« — b) sin i (tt -|- ^) = (^ sin i (a — (T). 



-\- b tan ^ (g -f /3) __ tan I y 



— b tan J (a — /3) tan ^ (a — )8)' 



a^ ■=. b"^ -\- r — 2 be cos az= {b -\- cf — ^b c cos" ^ a. 



tan ^ a = i/' 



(, -b){s- c) 



s {s — a) s — a 



-J (s-a)(s-b)(s-c\ 



A 1 / • ff'^ sin /? sin y . - o • 



A=^\ab%\r\ y = • —. = 2 y?" sin a sin B sin y 



^ ' 2 sin a '^ ' 



= 1^ cot ^ a cot ^ ^ cot i y = y'' X (i- — (7) (j- — b) {s — c) 

 =zrs^=\abc JR. 



