Question

In △ABC, M and N are the mid-points of BC and AC. If MN = 2.6 cm, ∠CNM = 30°, find the length of AB and the size of ∠BAC.

A. AB = 5.2 cm, ∠BAC = 60°.
B. AB = 2.6 cm, ∠BAC = 30°.
C. AB = 5.2 cm, ∠BAC = 30°.
D. AB = 2.6 cm, ∠BAC = 60°.

Answer 1

The correct answer is C. AB = 5.2 cm, ∠BAC = 30° since M and N are mid-points making triangles MNC and AMN congruent, deducing AB is twice the length of MN.

Step-by-step explanation:

The question involves the properties of triangles and specifically deals with concepts related to mid-points and triangle congruence. In △ABC, M and N are the mid-points of BC and AC respectively, so triangle MNC is congruent to triangle AMN by the Side-Angle-Side postulate since MN is equal to itself, ∠CNM is equal to ∠ANM, and MC is equal to MA because M is the mid-point of AC. Since MN equals 2.6 cm, which is half of AB, it follows that AB must be 5.2 cm. Considering the given angle of 30° at CNM, and since the triangles are congruent, the corresponding angle at BAC must also be 30°.

Therefore, the correct answer is C. AB = 5.2 cm, ∠BAC = 30°.