geometry word problems

Question

a bookcase fits diagonally into a corner of a room. Each side uses the same amount of wall space. Front of bookcase is 54 inches wide. What angles are formed where the front of the bookcase touched the walls?

Answer 1

Hi Mary.

 

If I'm reading this correctly, the case forms an isosceles right triangle with the wall. We can assume the corner is a 90-degree angle, so the other two angles must add up to the remaining 90 degrees of the triangle.

 

Since the two sides of the right triangle are congruent, the angles opposite them must be congruent as well. So two congruent angles that add up to 90 degrees must each be 45 degrees.

 

The fact that the front (the hypotenuse of the triangle) is 54 inches doesn't matter here unless you're trying also to find the lengths of the 2 congruent sides (legs).

 

Hope this helps.

 

Matt