Using a pair of compasses , pencil and ruler only, construct triangle ABC,in which AB=8cm, angle ABC=60°, angle CAB=45°. measure AC.
To construct triangle ABC, follow these steps:
Step 1: Draw a line segment AB with a ruler, making it 8cm long. This will be the base of the triangle.
Step 2: Place the point of the compass at point A, and open it to any convenient radius. Draw an arc that intersects line AB.
Step 3: Without changing the compass width, place the point of the compass at point B. Draw another arc that intersects the first arc we just made. Label this point of intersection as point P.
Step 4: Using a ruler, draw a line segment AP connecting point A to point P.
Step 5: Place the point of the compass at point A and open it to any convenient radius. Draw an arc that intersects line AP.
Step 6: Without changing the compass width, place the point of the compass at point P. Draw another arc that intersects the first arc we just made. Label this point of intersection as point Q.
Step 7: Using a ruler, draw a line segment AQ connecting point A to point Q.
Step 8: Angle ABC is given as 60°. To measure this angle accurately, use the ruler to draw a line segment from point B, making it a little longer than AB. From the endpoint of this segment, draw another line segment making an angle of 60° with the first line segment.
Step 9: Let the intersection of the two line segments be point C.
Step 10: Measure the length of AC using the ruler. This will give you the length of segment AC.
That's it! You have constructed triangle ABC and measured the length of AC using a pair of compasses, pencil, and ruler only.