Plane trigonometry, by S.L. Loney.

44

TRIGONOMETRY.

From the last figure we have
BM2= AM2 +AB2,
i.e. 3x2- x= +3002.
300~/3,/6
x= 2 — 150. -75 x /6
=75 x 2-44949... =183-71... feet.
Also his original distance from the tower
x
=x cot 60~= = 75 x /2
>~3
=75 x (1-4142...)=106-065... feet.
EXAMPLES. VIII.
1. A person standing on the bank of a river observes that the angle
subtended by a tree on the opposite bank is 60~; when he retires 40 feet
from the bank he finds the angle to be 30~; find the height of the tree
and the breadth of the river.
2. At a certain point the angle of elevation of a tower is found to be
3
such that its cotangent is -; on walking 32 feet directly toward the tower
2
its angle of elevation is an angle whose cotangent is. Find the height
of the tower.
3. At a point A the angle of elevation of a tower is found to be such
that its tangent is -; on walking 240 feet nearer the tower the tangent
3
of the angle of elevation is found to be; what is the height of the
tower?
4. Find the height of a chimney when it is found that on walking
towards it 100 feet in a horizontal line through its base, the angular
elevation of its top changes from 30~ to 45~.
5. An observer on the top of a cliff, 200 feet above the sea-level,
observes the angles of depression of two ships at anchor to be 45~ and 30~
respectively; find the distances between the ships if the line joining them
points to the base of the cliff.