A.Construct triangle xyz in which xy=8.3 yz=11.9 and xyz=60
B.Construct m,the mid-point of xz
C.measure ym
I assume you know the rudiments of constructions. Making a 60° angle is easy.
Once that is done, just mark off X and Z at the proper lengths.
Then construct the perpendicular bisector of XZ to find M.
These are some of the very first constructions usually taught; if you are still stuck, google can provide many examples and discussions.
How to do perpendicular bisector
To construct triangle XYZ, follow these steps:
1. Draw a line segment XY of length 8.3 units.
2. Place the compass on point X and set the radius to 11.9 units.
3. Draw an arc intersecting XY at point Z.
4. Join points Y and Z to form the triangle XYZ.
To construct the midpoint M of line segment XZ, follow these steps:
1. Draw a straight line from point X to point Z.
2. Use a compass to measure the distance from point X to point Z.
3. Place the compass on point X and adjust the radius to half the length of XZ.
4. Draw an arc intersecting the line segment XZ at two points.
5. Mark the point of intersection between the arc and XZ as M.
6. Draw a straight line connecting points X and M.
To measure the length YM, follow these steps:
1. Use a ruler to measure the length of the line segment YM.
Start measuring from point Y and end at point M.
2. Read the measurement on the ruler to determine the length of YM.