In triangle ABC, height AD, divides the base of BC into segments BD = 2√3 cm and DC = 8 cm.

| June 19, 2021 | education

In triangle ABC, height AD, divides the base of BC into segments BD = 2√3 cm and DC = 8 cm. Angle ABC = 60 °. Find the sides of the trellis.

Find side BC. BC = BD + DC, BC = 8 + 2√3 cm. Consider a right-angled triangle ADB (angle D of a straight line). Find the hypotenuse AB, AB = BD / cos ABD, AB = 2√3 / (1/2) = 4√3 (cm). By the Pythagorean theorem, we find leg AD. AD ^ 2 = AB ^ 2-BD ^ 2, AD ^ 2 = (4√3) ^ 2- (2√3) ^ 2, AD ^ 2 = 16 * 3-4 * 3 = 12 * 3 = 36. Since the sides can only be positive, then AD = √36 = 6 (cm). Consider a triangle CAD (). Let us find the hypotenuse AC by the Pythagorean theorem. AC ^ 2 = AD ^ 2 + CD ^ 2, AC ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100. Since the sides can only be positive, then AC = √100 = 10 (cm).
Answer: 8 + 2√3, 4√3 and 10 cm.



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