Use trigonometric ratios to determine whether or not it is possible to construct triangle abc if b = 3, c = 5, and b = 45°. in your final answer, include all of your calculations.

This is proves that It is not possible to construct the triangle ABC with the measures given.

1) The length b is opposite to the angle B.

2) The least possible length b is obtained when the angle C is 90°.

3) When the angle C is 90°, the triangle ABC is a right triangle, the length c (whic is opposite to the angle C) is the hypotenuse, and the sine of angle B is:

sine (angle B) = opposite side / hypotenuse = b / c

4) Solve for b, when B = 45° and c = 5 to obtain the least possible value of b:

b = c * sine (angle B) = 5 * sin (45°) = 3.54

5) That leads to conclude that b can never be equal to 3, which proves that it is not possible to construct the triangle ABC with the given measures.

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