Plane trigonometry, by S.L. Loney.

214

TRIGONOMETRY.

[Exs. XXXIII.]

3. DE is a tower standing on a horizontal plane and ABCD is a
straight line in the plane. The height of the tower subtends an angle 0
at A, 20 at B, and 30 at C. If AB and BC be respectively 50 and 20 feet,
find the height of the tower and the distance CD.
4. A tower, 50 feet high, stands on the top of a mound; from a
point on the ground the angles of elevation of the top and bottom of the
tower are found to be 75~ and 45~ respectively; find the height of the
mound.
5. A vertical pole (more than 100 feet high) consists of two parts,
the lower being -rd of the whole. From a point in a horizontal plane
3
through the foot of the pole and 40 feet from it, the upper part subtends
an angle whose tangent is 2. Find the height of the pole.
6. A tower subtends an angle a at a point on the same level as the
foot of the tower and at a second point, h feet above the first, the
depression of the foot of the tower is 3. Find the height of the tower.
7. A person in a balloon, which has ascended vertically from flat
land at the sea level, observes the angle of depression of a ship at anchor
to be 30~; after descending vertically for 600 feet he finds the angle
of depression to be 15~; find the horizontal distance of the ship from the
point of ascent.
8. PQ is a tower standing on a horizontal plane, Q being its foot;
A and B are two points on the plane such that the z QAB is 90~, and AB
is 40 feet. It is found that
cotPAQ=-1 and cotPBQ=1.
10 2
Find the height of the tower.
9. A column is E.S.E. of an observer and at noon the end of the
shadow is North-East of him. The shadow is 80 feet long and the
elevation of the column at the observer's station is 45~. Find the height
of the column.
10. A tower is observed from two stations A and B. It is found to
be due north of A and north-west of B. B is due east of A and distant
from it 100 feet. The elevation of the tower as seen from A is the
complement of the elevation as seen from B. Find the height of the
tower.