A triangle has angle measures 40°, 60° and 80°.
If the measure of the longest side is 120inches, what is the length of the shortest side?





We don’t have a picture to measure for scale, so we will create a triangle that is the same shape. To do this we will need to get all three angles exactly right.

Go to https://www.geogebra.org/ click “geogebra math apps” on the top center
Select “geometry” from the sidebar
  • Click on the angle tool , and select “angle with a given size”

  • Click any two spots on the screen, and the program will ask you what size angle.

  • Make it 40°

  • You should then get 3 ponts on the screen with one of them having a 40° angle.


  • Click on the line tool and select “ray”.

  • Using the measured angle as the vertex, draw in the angle with two rays meeting at the 40° vertex.

  • As you drag the points around, the angle should stay 40°

  • Select the “angle with a given size” tool again, and click on the vertex, and one of the other points. Make the angle 60°

  • If the angle is going the wrong way, undo then try again, this time clicking the vertex, and the other point.

  • Your picture should look like this:12.jpg

  • Click on the point tool and select “Intersect”

  • Click on the two rays that touch (but don’t have a point where they intersect) and a point should appear.

  • You should now have a triangle.


  • Click on the polygon tool and draw the triangle using the three vertices. (you have to end by clicking on the same point you started with)

  • Right click on all the extra rays and uncheck “show object” so all you can see is the triangle and the two angle measures

  • Right click each of the vertices and select “show label”

  • You picture should look like this: (your letters may be different)


  • Select the angle measure tool

  • Click points A, C, B

  • If you did it right, that last angle should be 80°

  • Next we have to find the lengths of the sides:

  • Under the measurement tool (the same one you used to measure the angle, select “distance”


  • Click points A and B, and the length of AB should appear.

  • Repeat for all three sides of the triangle





Now you have a triangle that is proportional to the one in the question. Use it to answer the original question:


A triangle has angle measures 40°, 60° and 80°.
If the measure of the longest side is 120inches, what is the length of the shortest side?