Exercises for Chapter III Section 3

Do NOT use a calculator for any of these problems, give only exact answers. (See Preface)

1. (a) Reconsider Examples 2. After finding c with the Law of Cosines, use the Law of Sines and Arcsin to find then use subtraction to find

     (b) Why are the answers different from the correct answers given in Example 2?

     (c) What must be done to insure getting the correct answers in this type of problems?

2. Solve each of the following triangles (See Figure 1c) from the given information if possible. The results of Problems 5 and 6 of Exercises for Chapter III Section 1 may be helpful here.

     (a) and c = 12.

     (b) and c = 20. HINT: a < c in this case.

     (c) and c = 6. HINT: Use the Law of Cosines first to find one of the angles.

3. Solve the isosceles triangle in the figure to the right.

4. Show that if you are given two angles and a side which is not the included side, (AAS or SAA), the triangle is still determined. This is usually a corollary to the ASA theorem.

5. Why is AAA not a congruence theorem?

6. Show that SSA does not determine a triangle by finding two distinct triangles which satisfy and b = 10.