In triangle MKP, side MP = 16 cm. Side KP is twice the distance from point K to straight MP. A line b is drawn through
| February 11, 2021 | education
In triangle MKP, side MP = 16 cm. Side KP is twice the distance from point K to straight MP. A line b is drawn through point M, parallel to KP. find: a) angle КPM b) distance between straight lines b and КP.
Consider a right-angled triangle KOР, in which, by condition, the segment OC = KP / 2, that is, the leg OC, which lies opposite the angle P, is equal to half of the hypotenuse KP, then the angle KOR = KPM = 30.
Consider a right-angled triangle МНР, in which the angle МРН = 30, and the hypotenuse is equal МР = 16 cm. Then the leg МН, which lies opposite the angle 30, is equal to half of the hypotenuse МР.
MH = MR / 2 = 16/2 = 8 cm.
Answer: Angle KPM = 30, the distance between straight lines b and KP is 8 cm.
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