The aegis & intelligencer. [volume] (Bel Air, Md.) 1864-1923, 1878-03-22
Answer to w. $. BIS Problem.
NJ the E1itnr of Tile IRnie

~ He LLuHU " Inc <DgtS
SIR: We find over the signature w. S. B..
the following problem
"A tree leans due south; a line is measured
on level plane from its base due north so yards
and the angle of elevation to the top of the tire,
is found to be 30 degrees; from the last station
| q line is measured due west 10 or rs yards, the
| angle of elevation is again taken to the top o.
the tree and found to be 25 degrees. Required
the length of the tree and whether it be 70 or Il
yards to the last station to be geometrically
demonstrated"
B. b. has taken his problem out of the pro
vince OF geometry by giving numerical values to
the angles. Alphabetically and trigonometrically
the solution is as follows:
For the sake of cearness give attention to the
following lettering Put at the first station, sc
yards north of the foot of the tree; at The
second station, 7Oyards west of the first station
and at the top of the tree; put D at the foot OF
the tree, and at the foot of the perpendicular
dropped from the top of the tree. Now let q
equal the distance A g, and by the natural series
OF IS and 80 degrees find the length of the per.
perdicular Z in terms of a. Now since the
triangle b G is a right-angle triangle, square Q
and square 40, and express the square root OF
their sum, and we have the length of b C in
terms of 1and the base B. Now, by the natur-
al series of the angles 25 and 80 degrees, as in the
other vertical triangle, we find the value of the
same perpendicular z Il in terms of a. Wenow
have two expressions for the same line G E and
consequently an equation which gives the num-
erlcal value of e. that is, the length of the line
z and also the the height of the perpendicular
c E. Now the base line L, the length of the
tree d c, and other lines are found trigonometri-
cally, nd libitum.
Using 70 yards as base, the length of the tree
is 45.49 yards.
If IS yards be taken for the base the length of
the tree will be 9.S5 yards
We hope w 5 b. will consent to come forth
from the silence, to which he SAYS he is now re-
tired, and explain the possibility of determining
whether his base be 70 yards or Is yards, without
giving the inclination of the tree or some other
data If at 10 yards the angle of elevation be 25
degrees and at IS yards the angle by the same.
then in the last case the tree must be longera and
with greater inclination from the perpepdicu.
lar. If the angle of inclination In the tree had
been given, his requirement in regard to the
bases would have been determined. As we ex-
tend the base from 10 to IS yards the angle of
elevation remaining the same, the object must
nave greatest altitude; and as the tree is not lin.
tied, either in length or inclination boy can see
That the one base is just as good as the other As
The tree must not come above the line c pro-
duced, for the longer base, the tree must lave
both greater length and greater inclination from
the perpendicular
We must join with our friend, whom lie so
rldicules, and recommend to him the continued
study of the mathematics. We fear that in the
original problem some data were given which in
copying w. 5. b. has omitted or altered For
w. s. BIS Improvement in his favorite science we
recommend to him the solution of the following
problem, simple in expression and proper for be-
ginners
"a courier leaves the rear of moving army.
which is % miles in length, and rides to the 'front.'
he returns without loss of time and at uniform
rate, and reaches the rear just as the rear arrives
at the point where the front was when he set out
How far did the courier ride?n N.Y.
Oahldnd BOARDING School, FdllSton.