WOLFRAM|DEMONSTRATIONS PROJECT

8. Construct a Triangle Given the Lengths of Two Sides and the Length of the Altitude to One of Them

​
a
c
h
A
step 1
step 2
This Demonstration shows a construction of a triangle
ABC
given the lengths
a
​
and
c
of the sides
BC
and
AB
and the length
h
A
of the altitude from
A
to
BC
.
Construction
Draw a line segment
AB
of length
c
, and let
D
be the midpoint of
AB
.
Step 1: Draw the circle
σ
with center
D
and radius
c/2
. Measure out a point
E
on
σ
at distance
h
A
from
A
.
Step 2: Extend
BE
to
C
such that
BC=a
.
Verification
Since
ABE
is a right-angled triangle and
AE=
h
A
by construction,
AE
is the altitude to
BC
and has length
h
A
.
​