Construct a triangle ABC such that | AB|=8cm, angle CBA=45° and angle CAB=60°
It is easy to construct the angles, so put them at the ends of AB.
Where the rays from A and B intersect is C.
Confidence
To construct a triangle ABC with the given conditions, follow these steps:
1. Start by drawing a straight line segment XY of any convenient length.
2. Mark a point A on XY, which will act as the base of the triangle. Measure and mark a distance of 8 cm from point A towards one end of XY. Label this point as B.
3. Using a protractor, construct a 60° angle at point B. This will form the interior angle CAB of the triangle.
4. From point B, measure and mark a distance of 8 cm towards the other end of XY. Label this point as C.
5. Without changing the width of the compass, place the compass at point C and draw an arc that intersects line segment AB. Label the point of intersection as D.
6. Using a protractor, construct a 45° angle at point D. This will form the interior angle CBA of the triangle.
7. Finally, draw a straight line segment connecting point C to point A. This will complete the triangle ABC.
Now, triangle ABC has |AB|=8cm, angle CBA=45°, and angle CAB=60°.
To construct a triangle ABC with the given conditions, follow these steps:
Step 1: Draw a line segment AB of length 8 cm. This will be one side of the triangle.
Step 2: Place the compass point on point A and draw an arc with a radius of 8 cm. This arc will intersect line segment AB at point C.
Step 3: Without changing the compass width, place the compass point on point B and draw an arc that intersects the previously drawn arc at point D.
Step 4: Draw a line segment CD.
Step 5: Construct the perpendicular bisector of line segment CD. To do this, place the compass point on point C and draw an arc that intersects line segment CD on both sides. Repeat the process by placing the compass point on point D and drawing arcs that intersect the previously drawn arcs.
Step 6: Label the intersection of the two arcs as point E. This will be the midpoint of line segment CD.
Step 7: Draw a line segment from point E to point B. This line segment will be the perpendicular bisector of line segment CD.
Step 8: The line segment AE is one of the sides of the desired triangle.
Step 9: Set the compass width to a suitable length and place the compass point on point E. Draw an arc that intersects line segment AE at point F.
Step 10: Draw a line segment from point F to point C. This line segment completes the triangle ABC.
Now, you have constructed a triangle ABC with |AB| = 8 cm, angle CBA = 45°, and angle CAB = 60°.