Math Help Forum: loci

without using a setsquare or protractor draw a triangle abc in which bc=7cm angle b =90degrees and angle c =30degrees .Find a pt d on ac such that it is equidistant from both sides ab and bc .measure db.

Originally Posted by kasak

without using a setsquare or protractor draw a triangle abc in which bc=7cm angle b =90degrees and angle c =30degrees .

I presume we are to do this using straight edge and compass, also I will
assume we have a line segment of known length.

1. Draw a line and mark a point on it lable it b.

2. Mark off a length of 7cm from a alonf the line mark the end point c (will use your segment of known length, you should know how to do this)

3. At b construct a right angle, produce the line upwards.

4. At c construct a 60 degree angle of the appropriate orientation, now bisect it, and produce the line towards the line in 3 above.

5. Mark the point at which these lines meet a, and you are done.

Find a pt d on ac such that it is equidistant from both sides ab and bc .measure db.

RonL

Originally Posted by kasak

without using a setsquare or protractor draw a triangle abc in which bc=7cm angle b =90degrees and angle c =30degrees .Find a pt d on ac such that it is equidistant from both sides ab and bc .measure db.

1. Construct the triangle ABC as shown by CaptainBlack.

2. All points which are equidistant to the legs of an angle are located on the angle bisector.

Construct the angle bisector (blue line)

3. The point of intersection between AC and the angle bisector is the point which is equidistant to AB and BC and is placed on AC.