Degree Wide
Posted on Thursday, March 18, 2010 in Security Systems
A rectangle is 80 cm long and 20 cm wide. Find , to the nearest degree, the acute angle formed at th?
A rectangle is 80 cm long and 20 cm wide. Find , to the nearest degree, the acute angle formed at the intersection of the diagonals
If we draw a line through the center, parallel to the long side,
it bisects the desired angle.
Since it is parallel to the long side that half-angle
equals the angle the diagonal makes with the long side itself.
tan (that angle) = 20 / 80 = 1/4
arctan (1/4) = 14.0362435 degrees
Double that and you get 28.0724870 which,
rounded to whole degrees, is 28°.
arctan(4) = 75.9637565 degrees,
which is good, because that is the complement of the other angle.
So the obtuse angle in the middle is
151.93 or 152°.
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