Question

State how many triangles possible given the measurements

M b=7m
c=33

And

b=34 yd
c=28 yd

Thank you

Answer 1

7. one triangle

8. two triangles

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.)

_____

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.