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