Plane trigonometry, by S.L. Loney.

206

TRIGONOMETRY.

[Exs. XXXI.]

6. Given B=30~, c =150, and b=150^/3, prove that of the two
triangles which satisfy the data one will be isosceles and the other rightangled. Find the greater value of the third side.
Would the solution have been ambiguous had
B =30~, c = 150, and b =75?
7. In the ambiguous case given a, b, and A, prove that the difference
between the two values of c is 2 a2 - b2 sin2 A.
8. If a= 5, b =4, and A =45~, find the other angles, having given
log 2 = 30103, L sin 33~ 29' = 97520507,
and L sin 33~30' = 97530993.
9. If a =9, b= 12, and A =30~, find c, having given
log 2 = 30103, log 3 = -47712,
log 171= 2-23301, log 368 = 2-56635,
L sin 11~ 48' 39" = 9'31108, L sin 41~ 48' 39" = 982391,
and L sin 108~ 11' 21" = 9-977774.
10. Point out whether or no the solutions of the following triangles
are ambiguous.
Find the smaller value of the third side in the ambiguous case and
the other angles in both cases.
(1) A=30~, c=250 feet, and a=125 feet;
(2) = 30~, c=250 feet, and a=200 feet.
Given log 2 = -30103, log 6-03893 = -7809601,
L sin 38~ 41' = 9-7958800,
and L sin 8~ 41' = 91789001.
11. Given a =250,b= 240, and A = 72~ 4' 48", find the angles B and C,
and state whether they can have more than one value, given
log 25 = -3979400, log 2'4= -3802112,
L sin 72~ 4'= 9 9783702, L sin 72~ 5' = 99784111,
*and L sin 65~ 54'= 9-9606739.
12. Two straight roads intersect at an angle of 30~; from the point of
junction two pedestrians A and B start at the same time, A walking