EXERCISES FOR CHAPTER 1
 

1. Classify each of the following angles as acute, right, obtuse, or not possible in a triangle:

2. Tell which pairs of angles are possible in the same triangle and find the third angle in each such case:

(a) 90^o, 90^o;          (b) 100^o, 85^o;          (c) 50^o, 60^o;           (d) 30^o, 140^o.
 

3. Find both the exact value and a two decimal approximation (See Preface) for v in each of the following diagrams:
 

4. Of the following triples, first identify those which represent sides of a triangle. Of those, select the right triangles and identify them. Then pick out the 45^o, 45^o, 90^o triangles and the 30^o, 60^o, 90^o triangles:
 

(a)    (b) 2, 3, 11   (c) 5, 12, 13

(d) 8, 9, 11 (e) 3, 3,    (f) 1, 2,

(g) 1,  (h)    (i) 7.11, 9.48, 11.85

5. Given that  is similar to  find x and y.

6. Which angle in  is equal to angle A? 

7 (a) Is a triangle with sides  similar to one with sides 

(b) Is a triangle with sides 23.472, 41.144, 51.256 similar to one with sides 55.1592, 96.6884, 110.2004?
 

8. Which of the following pairs of triangles are similar? Justify your answers.
 
 

9. Given: angles A and A' are equal.  (a) Find u and v in terms of r, a, and b.  (b) If a = 2.6 and b = 1.1 find r, u, and v to 3 decimal places.

10. Are any two 30^o, 60^o, 90^o triangles similar? Justify your answer.
 

11. Explain why a triangle whose sides are of length  is a right triangle.
(Of course, a > 0 and b > 0.)
 

12. Complete the following table for converting certain degree measures to radians or, when read properly, radians to degrees:
 

in degrees	0o	30o	45o			120o		150o	180o
in radians	0

13. Given that  and  have the same direction and magnitude, and that  and  have the same direction and magniture, show that  and  have the same direction and magnitude.

14. Prove that AEFG is a parallelogram, give that  ABCD is a parallelogram, and

15. Let  in  Let a, b, and c stand for the lengths of sides opposite  and  respectively. Find:

(a) c when a = 5 and b = 12

(b) b when a = 8 and c = 17

(c) when  and c = 8

(d)  when  and c = 10.
 

16. Given a unit length, outline the construction with straightedge and compass of lengths of

(a) 2/3

(b)