SOLUTION: A bookcase fits diagonally into the corner of the room. The front of the bookcase is 54 in wide. Each side of the bookcase uses the same amount of wall space. What angles are forme

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Question 953957: A bookcase fits diagonally into the corner of the room. The front of the bookcase is 54 in wide. Each side of the bookcase uses the same amount of wall space. What angles are formed where the front of the bookcase touches the wall?
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
...If the corner is square (90 degrees), the two wall lengths of equal size and the front of the bookcase form an isosceles right triangle, so the angles are 45 degrees.
...More rigorously, Theorem Three states that in an isosceles triangle, the angles at the base are equal. In euclidean geometry, the triangle postulate states that the sum of the angles in any triangle is two right angles. Since the right angle measures one right angle, the two equal angles must sum one right angle (90 degrees), so each angle must be 45 degrees.
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