Plane trigonometry, by S.L. Loney.

208

TRIGONOMETRY.

EXAMPLES. XXXII.
17 1
1. If cos A =2 and cos C=-4, find the ratio of a: b: c.
22 14'
2. The angles of a triangle are as 1: 2:7; prove that the ratio of
the greatest side to the least side is ^/5 + 1: ^/5 - 1.
3. If A =45~, B = 75~, and C = 60~, prove that a + c /2 = 2b.
4. Two angles of a triangle are 41~ 13' 22" and 71~ 19' 5" and the side
opposite the first angle is 55; find the side opposite the latter angle,
given
log 55 = 17403627, log 79063 = 4-8979775,
L sin 41~ 13' 22"=9-8188779,
and L sin 71~ 19' 5" =9-9764927.
5. From each of two ships, one mile apart, the angle is observed
which is subtended by another ship and a beacon on shore; these angles
are found to be 52~ 25' 15" and 75~ 9' 30" respectively. Given
L sin 75~ 9' 30" = 9-9852635,
L sin 52~ 25' 15" = 9'8990055, log 1-2197 = '0862530
and log 12198 = -0862886,
find the distance of the beacon from each of the ships.
6. The base angles of a triangle are 22~~ and 112~~; prove that the
base is equal to twice the height.
For the following 5 questions a book of tables is required.
7. The base of a triangle being seven feet and the base angles
129~ 23' and 38~ 36', find the length of its shorter side.
8. If the angles of a triangle be as 5: 10: 21, and the side opposite
the smaller angle be 3 feet, find the other sides.
9. The angles of a triangle being 150~, 18~ 20', and 11~ 40', and the
longest side being 1000 feet, find the length of the shortest side.
10. To get the distance of a point A from a point B, a line BC and
the angles ABC and BCA are measured, and are found to be 287 yards
and 55~ 32' 10" and 51~ 8' 20" respectively. Find the distance AB.
11. To find the distance from A to P a distance, AB, of 1000 yards is
measured in a convenient direction. At A the angle PAB is found to be
41~ 18' and at B the angle PBA is found to be 114~ 38'. What is the
required distance to the nearest yard?