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MENSURATION. 1 95
To Find the Height in any Triangle when the Length
of the Three Sides is Given.
(See Fig. 2).
The base line is to the sum of the other fig. 2
two sides as the difference of the sides is to
the difference between the two parts of the
base line, on each side of the line measuring
the perpendicular height. If half this dif-
ference is either added to or subtracted
from half the base line, there will be obtained two right-angled
triangles, in which the base and hypothenuse are known and
the perpendicular may be calculated thus : Using Fig. 2 for an
example, and adding half the difference to half the base line,
this may be written in the formula:
Rule.
Multiply the sum of the sides by their difference and divide
this product by twice the base; to the quotient add half the
base ; square this sum (that is, multiply it by itself) ; subtract
this from the square of the longest side, and the square root of
the difference is the perpendicular height of the triangle.
Example.
In the triangle, Fig. 2, the sides are:
c = 12 inches.
a = 9 inches.
b = 6 inches ; find the perpendicular height x.
x = Jos _/ (9 + 6)X(9-6)
X
V 2 X 12
x= ^81-(lt + 6)2
x = Jsi — 7.S75 2
12 \2
81 — 62.015
x— J 18.985
x = 4.357 inches.
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