27b. Construct a Triangle Given Its Perimeter, an Angle and the Length of the Altitude to the Side Opposite the Angle
This Demonstration constructs a triangle given the perimeter , the angle at and the length of the altitude from to the base .[more]
This construction uses a previous method to construct a triangle given the length of the base , the opposite angle and the length of the altitude to the base.
1. Draw a triangle given the length of the base , the angle opposite the base and the length of the altitude from .
2. Let be the intersection of and the perpendicular bisector of . Similarly, let be the intersection of and the perpendicular bisector of .
3. Then the triangle satisfies the conditions.
By step 1, . Also, since is isosceles, . Similarly, . So .
Since , .
By step 1 and isosceles triangles, is the perimeter of .[less]
This construction was taken from .
 G. Polya, How to Solve It: A New Aspect of Mathematical Method, 2nd ed., Princeton, NJ: Princeton University Press, 1957.