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06 Dec 2019, 20:04
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18% (02:44) correct
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A point is randomly chosen inside the unit square ABCD such that angle APB is equal to x. What is the probability that angle x is obtuse ?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
A. 0.1
B. 0.2
C. 0.3
D. 0.4
E. 0.5
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Untitled.png [ 5.13 KiB | Viewed 9299 times ]
07 Dec 2019, 06:41
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nick1816
Now when will x be 90— when AB is a diameter and a semi circle is drawn with AB as diameter.
So, P can be anywhere on the semicircle.
Any point within this semi circle will give an angle >90.
Probability =area of semicircle/area of square
Area of semicircle =\(\frac{1}{2}*\pi*(\frac{AB}{2})^2=\frac{\pi*AB^2}{8}\)
Area of square = \(AB^2\)..
Probability =\(\frac{\pi*AB^2}{8AB^2}=\frac{\pi}{8}=\frac{22}{56}\)=~0.4
D
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14 Nov 2025, 11:35
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