SOLUTION: a shelf is built into the corner of a room whose walls meet at an angle of 120 degree. Find the area of the shelf space if its front edge is 24cm and the other two edges are equal.

Question 964063: a shelf is built into the corner of a room whose walls meet at an angle of 120 degree. Find the area of the shelf space if its front edge is 24cm and the other two edges are equal.

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Bisecting the angle of the wall to midpoint of front edge forms two 30-60-90 triangles.
1/2 the front edge is 12 cm and this is the long leg of the triangle. The ratio of long leg/short leg= so:
=6.93 cm is the short leg of the 30-60-90, which is the height of the triangle formed by the shelf, with the front edge as base.
Area=(1/2)(base)(height)
Area=1/2(24cm)(6.93cm)
Area=83.14 sq cm
ANSWER: The area of the shelf is 83.14 square centimeters.
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