Plane trigonometry, by S.L. Loney.

[Exs. XXXI.] SOLUTION OF TRIANGLES.

207

along one road at the rate of 5 miles per hour and B walking uniformly
along the other road. At the end of 3 hours they are 9 miles apart.
Shew that there are two rates at which B may walk to fulfil this
condition and find them.
For the following 3 examples, a book of tables will be required.
13. Two sides of a triangle are 1015 feet and 732 feet and the angle
opposite the latter side is 40~; find the angle opposite the former and
prove that more than one value is admissible.
14. Two sides of a triangle being 5374-5 and 1586-6 feet, and the
angle opposite the latter being 15~ 11', calculate the other angles of the
triangle or triangles.
15. Given A = 10, a= 2308-7, and b =7903 2, find the smaller value
of c.
189. Case IV. Given one side and two angles, viz.
a, B, and C.
Since the three angles of a triangle are together equal
to two right angles, the third angle
is given also. A
The sides b and c are now obtained cb
from the relations
b c a B C
sin B sin C sin A'
sin B sin C
giving b = -. and c = a
sin A' sin A
190. Case V. The three angles A, B and C given.
Here the ratios only of the sides can be determined
by the formulae
a b c
sin A sin B sin C
Their absolute magnitudes cannot be found.