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

.