B


1.  i?==90°-^  =  27°50'.
2.  -  =GotA:  .'.b^acotA.
a

3.  -  =sinA


a  =  c  sin  A,  and  c  =


sin^


log  b        =  log  a  -\-  log  cot  A
log  a        =    1.89209
log  cot  ^=    9.72262-10
log^»        =    1.61471
b        =  41.182


logc  =loga-|-cologsin^

log  a  =    1.89209

cologsin^=   0.05340
logc  =   1.94549

c  =88.204


THE    RIGHT    TRIANGLE.
26


Case  III.
Given  A  =  50°  2',  b  =  SS;  find  ^,  a,  c.
1.  ^  =  90°  — ^  =  39°  58'.
2.  -=tan^;  .-.a  =  6  tan  A

3.  -  =G0SJ.
G


■,  J)  =zcQ,o^A,  and  c  =


cos^


log  a        =  log  Z*  +  log  tan  A
logh         =      1.94448
log  tan  J  =    10.07670  —  10
log<^        =      2.02118
a        =  105.0


logC  =:log^  +  COlogCOS^

log^  =     1.94448

cologcos^=     0.19223

logc  =     2.13671

c  =137.0


Case  IV.
Given  c  =■  58.40,  a  =  47.55  ;  find  A,  B,  h.
1.  sinJ=--

c

2.  ^  =  90°  — A

3.  -=cot^:     .'.b  =  aGotA.
log  sin  A  =  log  a  +  colog  c
log  a        =1.67715
colog  c     =8.23359  —  10
log  sin  y1=:  9.91074  — 10

^  =  54°  31'

^  =  35°  29'


log  b        =  log  a  +  log  cot  A
log  a        =    1.67715
log  cot  ^=    9.85300-10
logb        =   1.53015
b        =  33.896


26


TRIGONOMETRY.
Case  V.
T


Given  a  =  40,

/

27;

B

find  A,  B,  c.
1.   tan^  =  ^-

0

-}

a
0

2.  ^=-90°-J.
3.  -  =  sin  A.
c

.*.  a  =csin^;.
6    ^^
Fig.  17.
