In triangle ABC, what is the length of AB?
(1) The length of BC is 5 and the length of AC is 12.
(2) Angle C = 90°.
This question asks us straightforward to find the length of AB in the triangle ABC. We must know the angles, or ratio of angles in the triangle and we must know one or some of the sides lengths.
Statement (1) tells us that the length of BC is 5 and the length of AC is 12 which is perhaps a trap that preempts one to conclude this the pythagoren triplet 5 : 12 : 13- though this is not necessarily true because we do not know what the corresponding angles to these sides are and we do not know which angle is the hypotenuse. Insufficient.
Statement (2) tells us that the length of Angle "C" is 90 , but we neither have the measure or ratio of the other two angles nor a side length(s). Insufficient.
Statement (1) and (2) taken together allow us to find the ratio of the sides and the angles by testing values, such as the Pythagoren triplet 5:12 :13- hence both statements taken together are sufficient.
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