In triangle ABC, point K is taken on side AC, and point M on side BC so that angle B = angle MKC
| March 16, 2021 | education
In triangle ABC, point K is taken on side AC, and point M on side BC so that angle B = angle MKC, AK = 3cm, KC = 12cm, MC = 10cm. Find the BC side.
Let us prove that triangles ABC and KMC are similar.
By condition, the angle ABC is equal to the angle MKC, and the angles BCA and MCK are common, therefore the triangles ABC and KMC are similar in the first attribute, in two angles.
The sought side BC is equal to the sum of the segments CM + BM, let the segment BM = X cm, AC = AK + KC = 15 cm, then:
AC / MC = (MC + X) / KC.
15/10 = (10 + X) / 12.
10 * (10 + X) = 15 * 12.
10 * X + 100 = 180.
10 * X = 80.
X = 8 cm.
BM = 8 cm, then BC = 8 + 10 = 18 cm.
Answer: Side BC = 18 cm.
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