In a right-angled triangle ABC, angle C = 90 °, angle B-30 °, BC-18cm, CK perpendicular to AB, KM perpendicular to BC. Find MB.
Consider a right-angled triangle CKB, in which the angle K is straight, since CK is the height to AB, the angle B = 30 by condition.
Then the leg CK lies opposite the angle 30, which means that its length is equal to half of the hypotenuse BC.
CK = BC / 2 = 18/2 = 9 cm.
Consider a right-angled triangle CKM, in which the angle M = 90 according to the condition, Angle K = 90 – BKM = 90 – 60 = 30.
Then the CM leg lies opposite an angle of 30 and, accordingly, is equal to half of the CК hypotenuse. CM = CK / 2 = 9/2 = 4.5 cm.
Determine the length of the segment MB. MB = BC – CM = 18 – 4.5 = 13.5 cm.
Answer: Segment MB = 13.5 cm.
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