Construction of Triangle ABC:

To construct a triangle ABC with AC = 6 cm, Angle A = 60 degrees, and Angle B = 90 degrees, we can follow the steps below:

Step 1: Draw a line segment AB:
Take a ruler and draw a line segment AB of any convenient length. This will be the base of the triangle.

Step 2: Construct a perpendicular bisector of AB:
Using a compass, place the needle on point A and draw an arc above and below the line segment AB. Repeat the same process by placing the needle on point B. The arcs should intersect at two points. Connect these two points with a straight line. This line will be the perpendicular bisector of AB.

Step 3: Mark a point C on the perpendicular bisector:
Using a compass, measure a distance of 3 cm on the perpendicular bisector from the midpoint of AB. This will be point C.

Step 4: Draw lines connecting point A to points B and C:
Using a ruler, draw a line connecting point A to point B. This will be the hypotenuse of the triangle.

Next, draw a line connecting point A to point C. This will be one of the legs of the triangle.

Step 5: Measure the angles:
Using a protractor, measure Angle A and Angle B to ensure they are 60 degrees and 90 degrees respectively.

Step 6: Label the triangle:
Label the points of the triangle as A, B, and C.

Step 7: Verify the measurements:
Measure the length of AC to ensure it is 6 cm.

Step 8: Congratulate yourself on constructing Triangle ABC!

Summary:
By following these steps, you can construct a triangle ABC with AC = 6 cm, Angle A = 60 degrees, and Angle B = 90 degrees. Remember to use a ruler, compass, and protractor accurately for precise measurements. Double-check your measurements and congruence of angles to ensure the triangle is constructed correctly.