1. Construct a Triangle Given the Length of the Base, the Difference of the Base Angles and the Foot of the Altitude to the Base
This Demonstration constructs a triangle given the length of its base, the difference of the base angles and the foot of the altitude from to the base.[more]
Step 1: Draw a horizontal line of length and the foot of the altitude from . Measure out a point so that , so that is the midpoint of .
Step 2: Draw a vertical line through .
Step 3: Draw a circle with center so that the central angle .
Step 4: Let the intersections of and , if they exist, be and . Join , , and .
Then either of the two triangles or is a solution.
Step 5: Draw the triangle (dashed line).
Let and .
Consider the triangle (the verification for the triangle is similar). Because is the right bisector of , , so the angle . But this angle subtends the chord and is half of the central angle over , which is . So .[less]