**Solving
Right Triangles and Non-right Triangles**

**Solve
each right triangle (ie find all 6 parts)**

** **

1. a = 12, a = 35^{o}

2. c = 40, a = 23^{o}

3. a = 4, b = 7

4. c = 9, a = 7

5. b = 49^{o}, b = 3.2

6. c = 8, b = 35^{o}

7. a = 68^{o}, b = 4

8. a = 18, b = 12^{o}

9. b = 6, c = 9

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

** **

10.** ** b = 30^{o}, g = 17^{o}, c = .5

11. a = 42^{o}, b = 68^{o}, a = 23.5

12. g = 19^{o}, a = 17.2, c =
20.4

13. a = 20, b = 24, g = 30^{o}

14. a = 6, b = 8, c = 13

15. a = 3.9, c = 5.9, b = 130^{o}

^{ }

16. a = 16, b = 25, g = 129^{o}

17. a = 10, b = 12, g = 36^{o}

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 25^{o} 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 25^{o}. 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 32^{o}. 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 7^{o}12’
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.