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:
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?
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
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?