ff. A peraou on a tower can see the top of a pillar of
known altitude, from which he wbbes to know the distance,

and the height of the tower. He can see also an olgeci on
the horizontal plane from which be has formerly observed
the angular distance of the top of the pillar from that of
tiie tower. Shew how he may find the required distances,
having with him an instrument for measuring angles.
6. A. person on the top of a tower, the height of vrhich
is Ao feet, observes the angles of depression of two olgects
on the horizontal plane, which are in the same straight line
with the tower, to be scfi and 45" respectively. Find their
distances from each other and from the observer.
7. Three objects A, B, C, form an isosceles triangle
whose vertex is B, and whose angles are as the numbers
4, 1, I ; an observer walking from A toward C, measures
a base AD of a feet, and observes the angle BDC ; he then
advances io E,b feet further, and observes that the angle
BEC ' the supplement of BDC. From these observations
find the sides of the triangle.
8. A person walking from C to D on the horizontal
road can pltunly see the summit of a hill A from every
point except E, where he can just see it over a hill B. He
measures EC, and at C observes the angles of elevation of
B and A, as well as the angles ACB, ACE. At E he
observes the angle AEC. Shew how to find the heights of
the kills.
