Geogebra+Problem

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 [] 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:[[image:bolanmath/12.jpg width="266" height="178"]]


 * 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?