In the right-angled triangle ABC, the height CD is drawn to the hypotenuse AB; K is the middle of BC.

| March 4, 2021 | education

In the right-angled triangle ABC, the height CD is drawn to the hypotenuse AB; K is the middle of BC. Find AD and KD if the angle ABC = 60 degrees, AB = 8 cm.

Through the length of the hypotenuse AB and the angle ABC, we determine the length of the leg BC.

Cos60 = CB / AB.

CB = AB * Cos60 = 8 * 1/2 = 4 cm.

According to the condition, point K is the middle of the leg BC, then CK = BK = BC / 2 = 4/2 = 2 cm.

Since СD is the height of the triangle, then the BCD triangle is rectangular, and DK is its median, then, by the property of the median, the length is DK = СK = BK = 2 cm.

In the triangle ВDК DК = ВK, and the angle DВК = 60, then the triangle DВK is equilateral, ВD = ВK = DК = 2 cm.

Then AD = AB – BD = 8 – 2 = 6 cm.

Answer: The length of the segment AD is 6 cm, KD is 2 cm.



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