In a right-angled triangle ABC with a hypotenuse BC, angle B = 60 degrees, the height AB

In a right-angled triangle ABC with a hypotenuse BC, angle B = 60 degrees, the height AB is dropped from vertex A. What is DC if DB is 3 cm?

In a right-angled triangle ABD, determine the length of the leg AD.

tgABД = АD / DB.

АD = DB * tg60 = 3 * √3 cm.

In triangle ACD, angle ACD = (90 – 60) = 30, and in triangle ABD, angle BAD = (90-60) = 30, then in right triangles ACD and ABD acute angles are equal, which means that triangles are similar.

Then CD / AD = AD / DB.

CD = AD ^ 2 / DB = 9 * 3/3 = 9 cm.

Answer: The length of the CD segment is 9 cm.