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Answers to Math Exercises & Math Problems: Triangles and Properties of a Triangle

 

 

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1. P = 12 cm, A = sqrt(48) = 6.93 cm2, α = β = γ = 60°, α' = β' = γ' = 120°

 

2. α = β = 43°30', γ = 93°

 

3. 6 cm

 

4. 45°

 

5. a = 3 dm, b = 4 dm, α = 36°52', β = 53°08'

 

6. b = sqrt(136) = 11.66 cm, mb = sqrt(106) = 10.3 cm

 

7. a) h = 8.31 m
b) α = 77°46'

 

8. | MN | = 2( 6 +sqrt(6)) = 16.9 cm

 

9. a = b = 16 cm, c = 28 cm

 

10. | ACD | = 27°

 

11. α = 108°, β = 54°, γ = 18°

 

12. a = 15 cm, b = 22 cm, c = 17 cm, α = 42°54', β = 86°38', γ = 50°29'

 

13. α = 45°, β = 60°, γ = 75°, b = sqrt(3) = 1.73, c = 1.93

 

14. h = 325.7 m

 

15. w = 14.6 m

 

16. γ = 61°03', a = 30.28, b = 35.87, c = 33.94

 

17. P = 3 + sqrt(3) = 4.73, A = (sqrt(3))/2 = 0.87

 

18. a = 18.41 cm, b = 14.86 cm, c = 6.51 cm

 

19. b = 15.24, c = 10.66, α = 32°04', γ = 42°21'

 

20. A = 3.85

 

21. yes, γ = 91°18' > 90°

 

22. a = 20.86, b = 55.31, c = 68.06, γ = 119°32'

 

23. 105.16 N

 

24. d1 = 12.54 cm, d2 = 7.14 cm

 

25. a = sqrt(1008/5) = 14.2, b = sqrt(468/5) = 9.67, c = sqrt(1476/5) = 17.18

 

26. The triangle is right-angled.

 

27. r = 3

 

28. r = 17 cm

 

29. a = 13, h = 120/13 = 9.23, e = 10, f = 24

 

30. b = 15/4 = 3.75, c = 25/4 = 6.25

 

 

 

 

 

 

You might be also interested in:

- Perimeter and Area of Plane Figures

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- Geometric Construction Exercises

 

 
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