Solving Right Triangles and Non-right Triangles

 

Solve each right triangle (ie find all 6 parts)

 

1.  a = 12, a = 35o

 

2.  c = 40, a = 23o

 

3.  a = 4, b = 7

 

4.  c = 9, a = 7

 

5. b = 49o, b = 3.2

 

6.  c = 8, b = 35o

 

7. a = 68o, b = 4

 

8.  a = 18, b = 12o

 

9.  b = 6, c = 9

 

Solve each non-right triangle (ie find all 6 parts)

 

10.  b = 30o, g = 17o, c = .5

 

11. a = 42o, b = 68o, a = 23.5

 

12. g = 19o, a = 17.2, c = 20.4

 

13.  a = 20, b = 24, g = 30o

 

14.  a = 6, b = 8, c = 13

 

15.  a = 3.9, c = 5.9, b = 130o

 

16.  a = 16, b = 25, g = 129o

 

17.  a = 10, b = 12, g = 36o

 

18.  Romeo must rescue Juliet from her wicked uncle.  Juliet is trapped in a tower, which rises perpendicularly from the ground and has a window 10 feet above the ground.   Romeo needs to know what length of ladder he needs to prop up against Juliet’s window, to carry her away from the tower.  The angle of elevation between the ladder and the ground must be no greater than 25o or Romeo might lose his balance and drop Juliet.  Find the length of the shortest ladder that would work.

 

19.  It is common knowledge that Phineas Fogg and Passepartout started their 80-day journey around the world in a balloon.  Relatively unknown, though, is the fact that during the first minute of their journey they had a stowaway aboard whose name was Clyde.  After untying the balloon, which then went straight up, Mr. Verne bid the travelers adieu and started back to his library.  After walking a hundred feet in 1 minute, he turned around, pulled out his sextant, and measured the balloon’s angle of elevation; it was 25o.  At that very instant Fogg and Passepartout, unhappy about their slow ascent, threw overboard the trunk containing Clyde.  Poor Clyde was most grievously harmed. After another minute, when he had walked another hundred feet, Mr. Verne repeated his measurement; it was now 32o.  How much faster did the balloon rise in the second minute than in the first?  (The preceding information comes from Verne’s Works (vol 2) and The Complete Clyde (vol 68).

 

20.  Eratosthenes (circa 230 BC) made a famous measurement of the earth.  He observed that at noon at the summer solstice (the day on which the sun is farthest north) a vertical stick had no shadow at Syene (now Aswan), while at Alexandria (on the same meridian with Syene), the sun’s rays were inclined at  7o12’ to the vertical.  He then calculated the circumference of the earth from the known distance of 5000 stadia between Alexandria and Syene.    (Note:  because the earth is so far from the sun, you can always assume that the rays of the sun are parallel to each other whenever they strike the earth.)  Find the circumference of the earth in stadia.

 

21.  A field geologist standing 200 feet from a cliff with three exposed rock formations entered the sketch shown into his notebook.  Back in his office, he would like to know the thickness of each layer.  Assuming that you would also, find the thickness of each.