See Problem 2.

For Exercises 9–14, list the angles of each triangle in order from smallest to largest.

9. 
10. 
11. 
12. Δ A B C , cap delta eh b c comma  where A B = 8 , B C = 5 , eh b equals 8 , comma , b c equals 5 , comma  and C A = 7 c eh equals 7
13. Δ D E F , cap delta d e f comma  where D E = 15 , E F = 18 , d e equals 15 . comma . e f equals 18 . comma  and D F = 5 d f equals 5
14. Δ X Y Z , cap delta x y z comma  where X Y = 12 , Y Z = 24 , x y equals 12 . comma . y z equals 24 . comma  and Z X = 30 z x equals 30

See Problem 3.

For Exercises 15–20, list the sides of each triangle in order from shortest to longest.

15. 
16. 
17. 
18. Δ A B C , cap delta eh b c comma  with m ∠ A = 90 , m ∠ B = 40 , m angle , eh equals 90 , comma m angle , b equals 40 , comma  and m ∠ C = 50 m angle , c equals 50
19. Δ D E F , cap delta d e f comma  with m ∠ D = 20 , m ∠ E = 120 , m angle , d equals 20 , comma m angle , e equals 120 , comma  and m ∠ F = 40 m angle , f equals 40
20. Δ X Y Z , cap delta x y z comma  with m ∠ X = 51 , m ∠ Y = 59 , m angle , x equals 51 , comma m angle , y equals 59 , comma  and m ∠ Z = 70 m angle , z equals 70

See Problem 4.

Can a triangle have sides with the given lengths? Explain.

21. 2 in., 3 in., 6 in.
22. 11 cm, 12 cm, 15 cm
23. 8 m, 10 m, 19 m
24. 1 cm, 15 cm, 15 cm
25. 2 yd, 9 yd, 10 yd
26. 4 m, 5 m, 9 m

See Problem 5.

Algebra The lengths of two sides of a triangle are given. Find the range of possible lengths for the third side.

27. 8 ft, 12 ft
28. 5 in., 16 in.
29. 6 cm, 6 cm
30. 18 m, 23 m
31. 4 yd, 7 yd
32. 20 km, 35 km

B Apply

33. Think About a Plan You are setting up a study area where you will do your homework each evening. It is triangular with an entrance on one side. You want to put your computer in the corner with the largest angle and a bookshelf on the longest side. Where should you place your computer? On which side should you place the bookshelf? Explain.
    • What type of triangle is shown in the figure?
    • Once you find the largest angle of a triangle, how do you find the longest side?

    

34. Algebra Find the longest side of Δ A B C , cap delta eh b c comma  with m ∠ A = 70 , m ∠ B = 2 x − 10 , m angle eh equals 70 comma m angle b equals 2 x minus 10 comma  and m ∠ C = 3 x + 20 . m angle , c equals . 3 x plus 20 . .

Table of Contents