Question

State how many triangles possible given the measurements

Answer 1

Answer:

  7. one triangle

  8. two triangles

Step-by-step explanation:

When you are given two sides and one of the opposite angles, you can make a determination as follows:

• If the given angle is opposite the longest given side, there is one solution.
• If the given angle is opposite the shortest given side, there may be 0, 1, or 2 solutions.

For the latter case, the possibilities for sides b, c, and angle C are ...

  C > 90° . . . . . . . . no solution

  (b/c)sin(C) > 1 . . . no solution

  (b/c)sin(C) = 1 . . .  1 solution

  (b/c)sin(C) < 1 . . .  2 solutions

(The expression (b/c)sin(C) gives sin(B), so the value must lie within the range of the sine function in order for there to be any solution.)

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7. The given angle is opposite the longest given side. There is one solution.

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8. The given angle is opposite the shortest given side, so we compute

  (b/c)sin(C) = (34/28)sin(20°) ≈ 0.41

This is less than 1, so there are two solutions.