A pair of questions about Trigonometry?

Question

I have tried hundreds of times to solve these two exercises, but I do not achieve it. Can you please help me?

1. Construct a triangle ABC with a = 5,4 cm, b = 4,5 cm, and β = 50°. Why are there two answers? Calculate the pieces that are left.

2. a, b, α, and β are pieces of a triangle ABC. Fill the table (Longitudes in cm). Observe that there can be no, exactly one or two answers.

a = 8,3 / 7,6 / 5,8 / ? / 6,4 / 1,4

b = ? / 5,3 / 4,2 / 6,2 / 9,1 / 2,9

α = 34° / 112° / ? / 122° / 37° / 31°

β = 75° / ? / 52° / 24° / ? / ?

Answer 1

1) There is only one possible way to create a triangle (in Plane Geometry) given the lengths of 2 sides and the angle between them.

Your 'pieces that are left' question relates (I assume) to the use of some starting material that you forgot to define :-)

2) The word 'Longitudes' implies that these 'triangles' are being drawn in Spherical Geometry (actually, I assume, on an Earth like globe) ..

This makes the solution a LOT more complex :-)

Answer 2

All Answers Are To Two Decimal Places!!!

Q1) a=5.4, b=4.5, c=5.24

      Angle a=66.81

      Angle b=50

      Angle c=63.18

Q2)  

8.3     /  7.6     /  5.8    /  12.93   /   6.4     /   1.4

14.34  /  5.3     /  4.2    /  6.2      /   9.1     /    2.9

34      /  112     /  NS   /   122     /   37      /    31

75      /  40.28  /  52    /    24      /   58.84  /    NS

NS=No Solution

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