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

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

This Demonstration shows a construction of a triangle given the lengths and of the sides and and the length of the altitude from to .

ABC

a

c

BC

AB

h

A

A

BC

Construction

Draw a line segment of length , and let be the midpoint of .

AB

c

D

AB

Step 1: Draw the circle with center and radius . Measure out a point on at distance from .

σ

D

c/2

E

σ

h

A

A

Step 2: Extend to such that .

BE

C

BC=a

Verification

Since is a right-angled triangle and by construction, is the altitude to and has length .

ABE

AE=

h

A

AE

BC

h

A