In a right-angled triangle MKE, the angle is K = 90 degrees, KE = 8 cm, ME = 16 cm. KD is the height

univerkov | June 16, 2021 | education

In a right-angled triangle MKE, the angle is K = 90 degrees, KE = 8 cm, ME = 16 cm. KD is the height. Find the length of the segment DM.

By the Pythagorean theorem, KM ^ = ME ^ – KE ^ = 256 – 64 = 192, then KM = √ (192) = 8 √ (3).
sin (KME) = KE / ME = 0.5, angle KME = 30 degrees.
Since the angle MDK = 90 degrees, then MD = MK * cos (30) = 8 * √ (3) * √ (3) / 2 = 12 cm.
Answer: 12 cm.

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