30. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Difference of the Other Two Sides

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows how to construct a triangle given the length of side , the opposite angle at and the difference of the lengths of the other two sides .

[more]

Construction

1. Draw the segment of length .

2. Draw the circle with center so that .

3. Draw the circle with center and radius . Let the circles and meet at .

4. Let the point be the intersection of the ray and the perpendicular bisector of .

5. Then is the required triangle.

Verification

since it is an arc corresponding to the central angle . Since is an isosceles triangle with apex , and .

Thus .

[less]

Contributed by: Izidor Hafner (April 2018)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The problem was posed in [1, section IX, problem 2, solution pp. 291–292] and in [2, problem 2, p. 143].

References

[1] M. Bland, Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved, Cambridge: J. Smith, 1819.

[2] M. Bland and A. Wiegand, Geometrische Aufgaben für Hohëre Lehranstalten, Braunschweig: Schewetschke und Sohn, 1865. babel.hathitrust.org/cgi/pt?id=njp.32101076800687;view=1up;seq=143.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send