In a right-angled triangle ABC with a hypotenuse AB and an angle B equal to 60 degrees

univerkov | September 22, 2021 | education

In a right-angled triangle ABC with a hypotenuse AB and an angle B equal to 60 degrees, the height CD is drawn. Find AD if DB = 2cm.

In triangle ВСD the angle ВСD = (90 – 60) = 30. Then the leg ВD lies opposite the angle 30, then ВС = 2 * ВD = 2 * 2 = 4 cm.

Let the length of the segment AD = X cm, then AB = (X + 2) cm.

In a right-angled triangle ABC, the angle BAC = (90 – 60) = 30, then AB = 2 * BC.

(X + 2) = 2 * 4 = 8.

X = AD = 8 – 2 = 6 cm.

Answer: The length of the cut AD is 8 cm.

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