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

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

This Demonstration constructs a triangle given the length of the base , the angle at and the length of the altitude from to the base.

ABC

c

AB

γ

C

h

C

Construction

1. Draw a line segment of length .

AB

c

2. Draw the point so that the angle equals and . Draw the circle with center through and .

S

∠ASB

2γ

AS=BS

σ

S

A

B

3. Draw a line parallel to at distance . The third point of the triangle is the intersection of and .

ρ

AB

h

ABC

σ

ρ

Verification

The angle at is , since the central angle that subtends equals .

c

γ

AB

2γ