4.  What  condition  must  be  fulfilled  by  the  lengths  of  the
three  lines  a,  b,  c  (Fig.  2)  in  order  to  make  them  the  sides  of
a  right  triangle  ?     Is  this  condition  fulfilled  in  Example  3  ?

5.  Find  the  values  of  the  functions  of  A,  if  a,  b,  c  respec-
tively have  the  following  values  :

(i.)  2mn,  m^  —  n^,  m^-\-n^,  (iii.)  pqr,  qrs,  rsp.
...  ^     2x7/        ,       x^-\-ip'  ..    .    mn   mv    nr

(ii.)  — ^,x-\-y, — ^^-  (iv.)  — , — , —

^    ^   X  —  y  X  —  7/  ^     ^   pq     sq    ps

6.  Prove  that  the  values  of  a,  b,  c,  in  (i.)  and  (ii.),  Example
5,  satisfy  the  condition  necessary  to  make  them  the  sides  of
a  right  triangle.
7.  What  equations  of  condition  must  be  satisfied  by  the
values  of  a,  b,  c,  in  (iii.)  and  (iv.),  Example  5,  in  order  that
the  values  may  represent  the  sides  of  a  right  triangle  ?

Compute  the  functions  of  A  and  B  when,


8.  a  =  24,  &  =  143.  11.    a=4^^,    b=-J 2pq.
9.  a  =  0.264,  c  =  0.26^.        12.    a=V^+^,    c=p^q.
10.  &  =  9.5,  c  =  19.3.  13.   b=2^^,  c=p-\-q.
Compute  the  functions  of  A  when,

14.  a  =  2b,  16.    a-\-b  =  ^c.
15.  a  =  fc.  17.    a  —  b  =  ^.
18.  Find  a  if  sin  ^  =  f  and  c  =  20.5.
19.  Find  b  if  cos  A  =  0.44  and  c  =  3.5.
20.  Find  a  if  tan  ^  =  -y-  and  b  =  2j\.
TRIGONOMETRIC    FUNCTIONS.  1

21.  Find  5  if  cot  ^  =  4  and  a  =  17.
22.  Find  c  if  sec  ^  =  2  and  b  =  20.
