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ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α ?

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ABCD is a square and point P inside the square is such that PCD is an equilateral triangle. Find the angle α

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posted Feb 9, 2017 by anonymous

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3 Answers

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15 DEGREES height of the equilateral triangle is 0.866 times the base. let the base be unity so the height is 0.866 leaving the perpendicular distance from P to AB as 1-.866=0.134 so that alpha is tan inv(0.134/0.5) or 15 degrees.

answer Feb 10, 2017 by Kewal Panesar
0 votes

Alpha is equal to 15 degree
Suppose let the side of equilateral triangle be x and this square has also side lengths equal to x . �DPA is isosceles as DP=DA =x. Now
In triangle DPA
2(90-alpha) + 30 = 180
Therefore solving we get
Alpha equals to 15

answer Feb 12, 2017 by Sachite Anand
2*(90-ALPHA)+30=180
OR 2*(90-ALPHA)=150 OR
90-ALPHA=150/2=75
ALPHA=90-75=15
0 votes

PC=BC
angle PCB = 30
angle CBP = angle CPB = 1/2(180-30)=75
angle APB = 360 - (75+60+75) = 360 - 210 = 150
angle α = 1/2(180 - 150) = 30/2 = 15

answer Jul 29, 2018 by Halil Akansel



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