ABCA1B1C1 – regular triangular prism. Point O is the intersection point of the medians of the A1B1C1 face, and point P is the midpoint of the edge AB. Calculate the degree measure of the angle between the straight line PO and the plane AA1B, if it is known that the length of the median of the base of the prism is 9 cm, and PO = 6 cm.
Since, by condition, the prism is correct, an equilateral triangle lies at its base.
By the property of the medians, the point of their intersection divides the median in a ratio of 2/1 starting from the top, then C1O / HO = 2/1.
С1Н = 9 cm, then HO = 9 – С1О.
C1O = (9 – C1O) * 2.
3 * C1O = 18.
C1O = 6 cm.
OH = 9 – 6 = 3 cm.
The side faces of the prism are perpendicular to the base, then the HP segment is perpendicular to the OH segment, and the OHP triangle is rectangular.
Let us determine the required angle РОН.
SinРON = OH / OP = 3/6 = 1/2.
Angle POH = 300.
Answer: The angle is 300.
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