27a. Construct a Triangle Given a Side, the Length of the Altitude to It and the Opposite Angle

c

1.1

γ

1

h

0.6

steps

1

2

3

This Demonstration constructs a triangle

ABC

given the length

c

of the base

AB

, the angle

γ

at

C

and the length

h

of the altitude from

C

to the base.

Construction

1. Draw a line segment

AB

of length

c

.

2. Draw the point

S

so that the angle

∠ASB

equals

2γ

and

AS=BS

. Draw the circle

σ

with center

S

through

A

and

B

.

3. Draw a line

ρ

parallel to

AB

at distance

h

. The third point of the triangle

ABC

is the intersection of

σ

and

ρ

.

Verification

The angle at

c

is

γ

, since the central angle that subtends

AB

equals

2γ

.