Discussion
For which of the following measurements, the construction of triangle ABC can be done ?
Answer: C
The triangle can be constructed with AB = 8 cm, BC = 4 cm, \(\angle BCA = 90^\circ\), \(\angle ABC = 60^\circ\).
With the right angle at C, AB is the hypotenuse, and \(\cos 60^\circ = \frac{BC}{AB} = \frac{4}{8} = \frac{1}{2}\), so the four measurements agree and the triangle exists.
The others fail. In option 2, 3 + 4 = 7, so the sides cannot form a triangle. In option 4, AC = BC needs the angles at A and B to be equal, but the angle at B is 25° and the one at A is 35°. In option 1, two sides and the included 130° already fix the triangle, and its angle at A comes out near 27°, not 25°.
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