Geometry basic problem

Question

If I have a triangle with given: $b-c=3 \space\text{cm}$, $a=6\space \text{cm}$ and $\alpha$ is $30^\circ$, how do I draw this? Please help me by telling me where I can find this type of exercises online with explanations. Thank you!

Answer 1

Draw some generic triangle:

Then fill in what you know. $A=30\text{ degrees}$, $a=6\text{ cm}$ and $b-c=3\text{ cm}$. That means we can say $c=b-3\text{ cm}$

You can solve for $b$ using the Law of Cosines. Then from $b$ you can find $c$.

Answer 2

Step 1. Draw a line 3 units long (PQ).

Step 2. Draw another line 6 units long (PR) such that the angle between the two is 30 degrees.

(Hope that drawing a 30 degrees angle should not be a problem.)

Step 3. Join the endpoints of these two lines (QR).

Step 4. Produce the 3-unit line to certain extend (PQ... ).

Step 5. Draw MN, the perpendicular bisector of QR such that MN cuts the PQ produced at S.

Step 6. Join SR.

Triangle PRS is the required satisfying the given conditions (1) one side is 6; (2) one angle is 30 degrees (3) the difference between the other 2 sides is 3.