Question

Draw and label a triangle ABC where a = 23.5m, b = 19 cm, and ZA° = 152°. Solve all the missing sides and angles of triangle ABC.

Answer 1

In triangle ABC, where a = 23.5m, b = 19,cm, and
`\(\angle A = 152^\circ\)`, it is not possible to construct a valid triangle with these side lengths and angle measure. The given values violate the triangle inequality and the angle sum property, making the construction impossible.

Step-by-step explanation:

Firstly, according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, let's consider sides a, b, and the unknown side c. The triangle inequality would be expressed as
`\(a + b > c\), \(a + c > b\), and \(b + c > a\)`. However, with
`\(a = 23.5\,m\)` and b = 19 cm, the sum of these sides is less than c, violating the triangle inequality.

Secondly, the given angle measure
`\(\angle A = 152^\circ\)` is also problematic. The sum of the interior angles of a triangle is always
`\(180^\circ\)`, and an angle measure of
`\(152^\circ\)` for one angle exceeds the allowable range. In a valid triangle, all interior angles must be less than
`\(180^\circ\)`. The given value of
`152^\circ\) for \(\angle A\)` further indicates an inconsistency that prevents the construction of a triangle.

In conclusion, the provided values for side lengths and angle measure do not satisfy the conditions for a valid triangle. It is essential to check the triangle inequality and angle sum properties when attempting to construct a triangle with given specifications. In this case, the given values lead to contradictions, and a triangle with the specified parameters cannot be drawn.