Solve the given triangles by finding the missing angle and other side lengths.

Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

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Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...

  B = 180° -A -C = 28°

The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...

  side = sin(opposite angle)×((reference side)/sin(reference angle))

Note that the factor in italics remains the same for both remaining sides.

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In the first problem, this becomes ...

  a = sin(112°)·14/sin(28°) ≈ 27.65

  c = sin(40°)·14/sin(28°) ≈ 19.17

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The remaining problems are worked in similar fashion.

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Comment on triangle solutions

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.

The answer to your question is below

Step-by-step explanation:

First picture

1.- Find B

The sum of the internal angles in a triangle equals 180°

    40° + 112° + B = 180°

    B = 180 - 40 - 112

    B = 28°

2.- Find c using law of sines

           c = 19.2

2.- Find a using law of sines

    a = 27.65

Second picture

1.- Find B

The sum of the internal angles in a triangle equals 180

       A + B + C = 180

      B = 180 - 15 - 45

      B = 120°

2.- Find a

           a = 163.3

3.- Find c

           c = 59.8

Picture 3

1.- Find A

The sum of the internal angles in a triangle equals 180°

    A + B + C = 180°

    A = 180 - 162 - 5

    A = 13°

2.- Find b

           b = 0.39

3.- Find c

             c = 1.37

step-by-step explanation:

the true statements are:

r = set of real numbers

n = set of natural numbers, 1,2,

w = n u{0} = {0,1,}