# 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

posted Feb 9, 2017

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

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
2*(90-ALPHA)+30=180
OR 2*(90-ALPHA)=150 OR
90-ALPHA=150/2=75
ALPHA=90-75=15

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

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